Recent content by kewljcs

to paraphrase question 1 : Prove that a finite Abelian group fails to be cyclic if and only if it has a subgroup isomorphic to Zp × Zp , for some prime p .

so, are you all saying that the first question is wrong? 1. If G is a finite group that does not contain a subgroup isomorphic to Z_p X Z_p for any prime p. prove that G is cyclic im still lost now. :/

well, if G is cyclic in the end, then we know that it is abelian. but I am not sure if we can use what we're trying to prove to do that :/

u mean for the 1st question? also, is my solution to the 2nd question correct?

im still lost about the first one. we didnt learn about that classification theorem which u mentioned.

i think i got the second one. since the mapping is from G to itself, the order is the same, so we're showing that the kernel of this mapping is 0. right? so i said that suppose x belongs to the kernel of the mapping, we want to show that x must be the identity, e. this implies that the...

1. If G is a finite group that does not contain a subgroup isomorphic to Z_p X Z_p for any prime p. prove that G is cyclic im stumped. i don't understand the 'does not contain a subgroup isomorphoc to Z_p X Z_p part. ive tried using cauchy's theorem for abelian group: if G is a finite...