Subgroup of finite index in mathematical writing
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I have a question about mathematical writing. A group G can have a subgroup H and every subgroup H has a so called index in G, which is a number (finite or infinite) and depends on both G and H and is written [H : G].
Which of the following two version is better?
A: For every subgroup H of finite index in G there exists a subgroup J of finite index in H such that ...
or
B: For every subgroup H in G of finite index there exists a subgroup J in H of finite index such that ...
I personally find the first one more logical but the second one better to read because it is immeditately clear that H is a subgroup of G. Is it bad style in the second version to write "of finite index" after specifying the subgroup itself?
mathematics
asked 2 days ago
abenthyabenthy
1011
New contributor
abenthy is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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add a comment |
I have a question about mathematical writing. A group G can have a subgroup H and every subgroup H has a so called index in G, which is a number (finite or infinite) and depends on both G and H and is written [H : G].
Which of the following two version is better?
A: For every subgroup H of finite index in G there exists a subgroup J of finite index in H such that ...
or
B: For every subgroup H in G of finite index there exists a subgroup J in H of finite index such that ...
I personally find the first one more logical but the second one better to read because it is immeditately clear that H is a subgroup of G. Is it bad style in the second version to write "of finite index" after specifying the subgroup itself?
mathematics
asked 2 days ago
abenthyabenthy
1011
New contributor
abenthy is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
2
I'd split up the noun phrases differently. For every subgroup of finite index H in G, there exists a subgroup of finite index J in H, such that ...
– John Lawler
2 days ago
You will probaly get more accurate advice if you ask this on a specialist website, like math.SE because they'll know their own style much better. Also, look at how other mathematicians write it (google subgroup finite index). That said. rewording a lot more may help (like John's comment). But frankly, both are fine. I might be more likely to say subgroup H of G, but people use in all the time too.
– Mitch
2 days ago
@JohnLawler Thank you, I like this too and I think I will use this version of yours now. The reason I did not include it in the first place is that I initially thought one might mistake "of finite index H" to mean that H itself should be the index, but I think the danger is probably very low, especially because H is an uppercase letter and numbers are usually denoted by lowercase letters.
– abenthy
yesterday
add a comment |
I have a question about mathematical writing. A group G can have a subgroup H and every subgroup H has a so called index in G, which is a number (finite or infinite) and depends on both G and H and is written [H : G].
Which of the following two version is better?
A: For every subgroup H of finite index in G there exists a subgroup J of finite index in H such that ...
or
B: For every subgroup H in G of finite index there exists a subgroup J in H of finite index such that ...
I personally find the first one more logical but the second one better to read because it is immeditately clear that H is a subgroup of G. Is it bad style in the second version to write "of finite index" after specifying the subgroup itself?
mathematics
asked 2 days ago
abenthyabenthy
1011
New contributor
abenthy is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
I have a question about mathematical writing. A group G can have a subgroup H and every subgroup H has a so called index in G, which is a number (finite or infinite) and depends on both G and H and is written [H : G].
Which of the following two version is better?
A: For every subgroup H of finite index in G there exists a subgroup J of finite index in H such that ...
or
B: For every subgroup H in G of finite index there exists a subgroup J in H of finite index such that ...
I personally find the first one more logical but the second one better to read because it is immeditately clear that H is a subgroup of G. Is it bad style in the second version to write "of finite index" after specifying the subgroup itself?
mathematics
mathematics
asked 2 days ago
abenthyabenthy
1011
New contributor
abenthy is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 2 days ago
abenthyabenthy
1011
New contributor
abenthy is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 2 days ago
abenthyabenthy
1011
New contributor
abenthy is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 2 days ago
abenthyabenthy
1011
asked 2 days ago
abenthyabenthy
1011
1011
New contributor
abenthy is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
abenthy is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
abenthy is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
2
I'd split up the noun phrases differently. For every subgroup of finite index H in G, there exists a subgroup of finite index J in H, such that ...
– John Lawler
2 days ago
You will probaly get more accurate advice if you ask this on a specialist website, like math.SE because they'll know their own style much better. Also, look at how other mathematicians write it (google subgroup finite index). That said. rewording a lot more may help (like John's comment). But frankly, both are fine. I might be more likely to say subgroup H of G, but people use in all the time too.
– Mitch
2 days ago
@JohnLawler Thank you, I like this too and I think I will use this version of yours now. The reason I did not include it in the first place is that I initially thought one might mistake "of finite index H" to mean that H itself should be the index, but I think the danger is probably very low, especially because H is an uppercase letter and numbers are usually denoted by lowercase letters.
– abenthy
yesterday
add a comment |
2
I'd split up the noun phrases differently. For every subgroup of finite index H in G, there exists a subgroup of finite index J in H, such that ...
– John Lawler
2 days ago
You will probaly get more accurate advice if you ask this on a specialist website, like math.SE because they'll know their own style much better. Also, look at how other mathematicians write it (google subgroup finite index). That said. rewording a lot more may help (like John's comment). But frankly, both are fine. I might be more likely to say subgroup H of G, but people use in all the time too.
– Mitch
2 days ago
@JohnLawler Thank you, I like this too and I think I will use this version of yours now. The reason I did not include it in the first place is that I initially thought one might mistake "of finite index H" to mean that H itself should be the index, but I think the danger is probably very low, especially because H is an uppercase letter and numbers are usually denoted by lowercase letters.
– abenthy
yesterday
2
2
I'd split up the noun phrases differently. For every subgroup of finite index H in G, there exists a subgroup of finite index J in H, such that ...
– John Lawler
2 days ago
I'd split up the noun phrases differently. For every subgroup of finite index H in G, there exists a subgroup of finite index J in H, such that ...
– John Lawler
2 days ago
You will probaly get more accurate advice if you ask this on a specialist website, like math.SE because they'll know their own style much better. Also, look at how other mathematicians write it (google subgroup finite index). That said. rewording a lot more may help (like John's comment). But frankly, both are fine. I might be more likely to say subgroup H of G, but people use in all the time too.
– Mitch
2 days ago
You will probaly get more accurate advice if you ask this on a specialist website, like math.SE because they'll know their own style much better. Also, look at how other mathematicians write it (google subgroup finite index). That said. rewording a lot more may help (like John's comment). But frankly, both are fine. I might be more likely to say subgroup H of G, but people use in all the time too.
– Mitch
2 days ago
@JohnLawler Thank you, I like this too and I think I will use this version of yours now. The reason I did not include it in the first place is that I initially thought one might mistake "of finite index H" to mean that H itself should be the index, but I think the danger is probably very low, especially because H is an uppercase letter and numbers are usually denoted by lowercase letters.
– abenthy
yesterday
@JohnLawler Thank you, I like this too and I think I will use this version of yours now. The reason I did not include it in the first place is that I initially thought one might mistake "of finite index H" to mean that H itself should be the index, but I think the danger is probably very low, especially because H is an uppercase letter and numbers are usually denoted by lowercase letters.
– abenthy
yesterday
add a comment |
1 Answer
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Mathematician here! I have seen the "less than or equal to" sign (⩽) occasionally used to mean "subgroup". So, you could write your statement as:
"Given a group G, for every H⩽G of finite index there exists J⩽H of finite index such that ..."
You could, of course, first define your own notation for subgroup and use that instead. I believe this is best because it makes it clear that you're talking about subgroups with finite index. I doubt that any mathematician reading this would have an issue understanding it.
answered 2 days ago
Brendan W. SullivanBrendan W. Sullivan
32617
add a comment |
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Mathematician here! I have seen the "less than or equal to" sign (⩽) occasionally used to mean "subgroup". So, you could write your statement as:
"Given a group G, for every H⩽G of finite index there exists J⩽H of finite index such that ..."
You could, of course, first define your own notation for subgroup and use that instead. I believe this is best because it makes it clear that you're talking about subgroups with finite index. I doubt that any mathematician reading this would have an issue understanding it.
answered 2 days ago
Brendan W. SullivanBrendan W. Sullivan
32617
add a comment |
Mathematician here! I have seen the "less than or equal to" sign (⩽) occasionally used to mean "subgroup". So, you could write your statement as:
"Given a group G, for every H⩽G of finite index there exists J⩽H of finite index such that ..."
You could, of course, first define your own notation for subgroup and use that instead. I believe this is best because it makes it clear that you're talking about subgroups with finite index. I doubt that any mathematician reading this would have an issue understanding it.
answered 2 days ago
Brendan W. SullivanBrendan W. Sullivan
32617
add a comment |
Mathematician here! I have seen the "less than or equal to" sign (⩽) occasionally used to mean "subgroup". So, you could write your statement as:
"Given a group G, for every H⩽G of finite index there exists J⩽H of finite index such that ..."
You could, of course, first define your own notation for subgroup and use that instead. I believe this is best because it makes it clear that you're talking about subgroups with finite index. I doubt that any mathematician reading this would have an issue understanding it.
answered 2 days ago
Brendan W. SullivanBrendan W. Sullivan
32617
Mathematician here! I have seen the "less than or equal to" sign (⩽) occasionally used to mean "subgroup". So, you could write your statement as:
"Given a group G, for every H⩽G of finite index there exists J⩽H of finite index such that ..."
You could, of course, first define your own notation for subgroup and use that instead. I believe this is best because it makes it clear that you're talking about subgroups with finite index. I doubt that any mathematician reading this would have an issue understanding it.
answered 2 days ago
Brendan W. SullivanBrendan W. Sullivan
32617
answered 2 days ago
Brendan W. SullivanBrendan W. Sullivan
32617
answered 2 days ago
Brendan W. SullivanBrendan W. Sullivan
32617
answered 2 days ago
Brendan W. SullivanBrendan W. Sullivan
32617
32617
add a comment |
add a comment |
abenthy is a new contributor. Be nice, and check out our Code of Conduct.
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2
I'd split up the noun phrases differently. For every subgroup of finite index H in G, there exists a subgroup of finite index J in H, such that ...
– John Lawler
2 days ago
You will probaly get more accurate advice if you ask this on a specialist website, like math.SE because they'll know their own style much better. Also, look at how other mathematicians write it (google subgroup finite index). That said. rewording a lot more may help (like John's comment). But frankly, both are fine. I might be more likely to say subgroup H of G, but people use in all the time too.
– Mitch
2 days ago
@JohnLawler Thank you, I like this too and I think I will use this version of yours now. The reason I did not include it in the first place is that I initially thought one might mistake "of finite index H" to mean that H itself should be the index, but I think the danger is probably very low, especially because H is an uppercase letter and numbers are usually denoted by lowercase letters.
– abenthy
yesterday