Subgroup of finite index in mathematical writing [closed]

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?

Solution 1:

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.