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July 21st, 2017, 12:06 AM  #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, 04:43 AM  #2 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,261 Thanks: 896 
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. 
July 21st, 2017, 06:26 AM  #3  
Newbie Joined: Jun 2017 From: Earth Posts: 17 Thanks: 0  Quote:
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.  
July 21st, 2017, 06:46 AM  #4 
Senior Member Joined: Oct 2009 Posts: 733 Thanks: 250 
I never really read the term invariant subgroup for this. I've always read normal.


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invariant subgroup, normal subgroup, nowadays, popular 
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