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July 21st, 2017, 12:06 AM   #1
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Is "invariant subgroup" more popular than "normal subgroup" nowadays?

Nowadays, is the usage of "invariant subgroup" more popular than "normal subgroup"?
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July 21st, 2017, 04:43 AM   #2
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I cannot speak for which is more "popular" but you seem to be under the impression that they are alternate terms for the same thing- they are not. An "invariant subgroup" is not at all the same as a "normal subgroup".

An "invariant subgroup", for a given transformation that maps the group to itself, is also mapped to itself. That is, if a is in an invariant subgroup, for transformation T, then Ta is also in that subgroup.

A "normal subgroup" is one such that its left and right cosets are the same (and so form a group themselves, the "quotient" group).

("subgroups", whether "invariant" or "normal" are properties of groups. This question should be in "Abstract Algebra", not "Linear Algebra".)

Last edited by Country Boy; July 21st, 2017 at 04:45 AM.
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July 21st, 2017, 06:26 AM   #3
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Quote:
Originally Posted by Country Boy View Post
I cannot speak for which is more "popular" but you seem to be under the impression that they are alternate terms for the same thing- they are not. An "invariant subgroup" is not at all the same as a "normal subgroup". ......
This is excerpted from "Schaum's outline of abstract algebra", 2nd edition:


This is excerpted from "Basic Algebra I", Nathan Jacobson, 1st edition:


PS: I'm sorry for the wrong subforum. Could any moderator please help me move this post to abstract subforum? Thanks.

[Note by moderator: done.]

Last edited by skipjack; July 21st, 2017 at 06:30 AM.
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July 21st, 2017, 06:46 AM   #4
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I never really read the term invariant subgroup for this. I've always read normal.
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