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Topic: Symmetric Group
Replies: 4   Last Post: Mar 1, 2011 12:24 AM

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qindars@gmail.com

Posts: 45
Registered: 1/12/07
Symmetric Group
Posted: Feb 28, 2011 2:12 PM
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Hi,

I am wondering why the group of all permutations on a set of n
elements is called a "symmetric group". (Sometimes knowing the origin
of a word helps me to better understand it). Neither wikipedia, nor
any of the texts I own (Hungerford's "Intro to Algera", Herstein, or
Dummit and Foote), directly answer this question.

I understand that the subgroup of all symmetries of a regular n-gon
are contained within S_n, but it seems to me that not all the elements
of S_n are in fact symmetries of a regular n-gon. (i.e. for n=4, I
don't think the permutation (1324) is part of the octic subgroup of
S_4).

Thank-you,
Fran



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