Recent content by jbarrera

Abstract Algebra Questions... I have two problems that I'm a little puzzled by, hopefully someone can shed some light. 1) Show that if H and K are subgroups of the group G, then H U K is closed under inverses. 2) Let G be a group, and let g ε G. Define the centralizer, Z(g) of g in G to...

I see how I can prove (a): I can say, Let g be an element in G which does not have finite order. Since (g)^k is in G for each value of k = 0, 1, 2, ..., we can conclude that we may find integers m and n such that (g)^m = (g)^n. If m > n, then g^(m-n) = e. Thus, m-n is the order of G and is...

Abstract Algebra Proof: Groups... A few classmates and I need help with some proofs. Our test is in a few days, and we can't seem to figure out these proofs. Problem 1: Show that if G is a finite group, then every element of G is of finite order. Problem 2: Show that Q+ under...