My Math Forum Is "invariant subgroup" more popular than "normal subgroup" nowadays?

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 July 20th, 2017, 11:06 PM #1 Newbie   Joined: Jun 2017 From: Earth Posts: 17 Thanks: 0 Is "invariant subgroup" more popular than "normal subgroup" nowadays? Nowadays, is the usage of "invariant subgroup" more popular than "normal subgroup"?
 July 21st, 2017, 03:43 AM #2 Math Team   Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902 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 03:45 AM.
July 21st, 2017, 05:26 AM   #3
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 Originally Posted by Country Boy 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 05:30 AM.

 July 21st, 2017, 05:46 AM #4 Senior Member   Joined: Oct 2009 Posts: 867 Thanks: 330 I never really read the term invariant subgroup for this. I've always read normal.

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