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It may be useful to clarify that <math>A_{n}</math> refers to the "group of even permutations of n symbols...and is called the alternating group of degree n" (p. 104), not the group of all permutations of a set of order n. Be that as it may, like Dfreidin (sorry) said, you can use it for groups, but not for elements (as I think we were to find orders for in the last homework). | It may be useful to clarify that <math>A_{n}</math> refers to the "group of even permutations of n symbols...and is called the alternating group of degree n" (p. 104), not the group of all permutations of a set of order n. Be that as it may, like Dfreidin (sorry) said, you can use it for groups, but not for elements (as I think we were to find orders for in the last homework). | ||
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Latest revision as of 15:51, 15 September 2008
Theorem 5.7 For n>1, A_n has order n!/2.
I was wandering how do you know when to use this cause I think I got confused on the last homework.
Remember, $ A_{n} $ is the group of all permutations of a set of order n, so the order is only n!/2 if you're looking at a group isomorphic to $ A_{n} $. In that case you can use it, but in any other case, you can't.
--Dfreidin 22:11, 14 September 2008 (UTC)
It may be useful to clarify that $ A_{n} $ refers to the "group of even permutations of n symbols...and is called the alternating group of degree n" (p. 104), not the group of all permutations of a set of order n. Be that as it may, like Dfreidin (sorry) said, you can use it for groups, but not for elements (as I think we were to find orders for in the last homework).
-Govind
