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Symmetric Group
Posted:
Feb 28, 2011 2:12 PM


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 ngon 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 ngon. (i.e. for n=4, I don't think the permutation (1324) is part of the octic subgroup of S_4).
Thankyou, Fran



