Recent content by mehrts

Thxs. He he he :!)

Let G be a group. Let 'a' be an element of G. Let e be the identity of G Prove that if a = a^-1 then a^2= e. Is the proof below correct ? Suppose a = a^-1. Then a^2 = aa = a(a^-1) = e.

Looks like the MATH 4160 assignment we had. :)

Thanks alot. :)

I think the correct answer would be that |W| = 0 or 1. Since the empty set contains the identity mapping. Is this correct ?

Thanks. So their is only one necessary and sufficient condition then ? Yup, the second part of the question was asking to prove the conditions are necessary and sufficient. :)

For example, Let S = {1, 2, 3, 4}. If W = {1} G_W = G_(W) = {(1),(2 3 4),(2 4 3),(3 4),(4 2),(2 3)}. IF W = {1, 2} G_W = {(1), (3 4)} G_(W) = {(1), (1 2), (3 4), (1 2)(3 4)} If W = {1, 2, 3} G_W = {(1)}. G_(W) = {(1), (2 3), (3 1), (1 2), (1 2 3),(1 3 2)}. So can I conclude that...

Click on the jpeg to see a bigger picture. http://img226.imageshack.us/my.php?image=untitled1nx0.jpg

We just started the topic and all I need is a hint on how to start the problem. :(

Oops sorry..... http://img226.imageshack.us/img226/2447/untitled1nx0.th.jpg

Let n be in |N. Let G denote S_n , the symmetric group on n symbols. Let W be a subset of {1, 2, ..., n}. Write down VERY simple necessary and sufficient conditions on |W|, for G_W to equal G_(W). We know G_W < G_(W) < G , but now what ?

Thanks that is what I thought. he he he :)

You're playing standard bridge with three other people. If you know that you and your partner have 10 hearts altogether, then what is the probability that the remaining 3 hearts are all in the same hand ? Is it comb(3,3)*comb(23,10)/comb(26,13) ? Since there is only 1 way of selecting 3...

Thxs I get it. :smile: I might post the solution up here later. :cool:

Prove that there is a mapping from a set to itself that is one-to one but not onto iff there is a mapping from the set to itself that is onto but not one-to -one. Since this is a 'iff' proof, so I must prove the statementlike two 'if' statements. Let g:S ---> S. Assume that g is 1-1...