group and set theory question?

Question

I have a couple problems I cannot really figure out

Let S be a set with an associative law of composition and with an identity elemment.  Prove that the subset of S consisting of invertible elements is a group.


Let S be any set.  Prove that the law of composition defined by a*b = a is associative.

and last one


Suppose that G is a group in which all elements x satisfy x^2 = e.  Prove that G is a commutative group.

(e is the identity element)

I know they are probably simple, but I do not know much about the associative law of composition, because for whatever reason its not in the book.
Thanks.

Anonymous · Accepted Answer

"Associative law of compostion" simply means that the operation is composition, and that the set is associative; and associative means (a*b)*c = a*(b*c), where * represents the operation.

If you have any more questions, ask me.

lacuesta · Answer

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group and set theory question?

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