Let G he an abelian group and H g G ordg is finite Show th

Let G he an abelian group and H = {g G | ord(g) is finite}. Show that H is a subgroup of G.

The start: let a^m=b^n=1. Then (ab)^mn=1.

Let H be the set of all elements of finite order.

(gh)^nm=(g)^nm . (h)^nm = (g^n)^m . h(^m)^n = 1^m .1^n=1.

(g1)^n. g^n=1=(g1)^n.

Therefore, H is a subgroup.

$Let G he an abelian group and H = {g G | ord(g) is finite}. Show that H is a subgroup of G.SolutionThe start: let a^m=b^n=1. Then (ab)^mn=1. Let H be the set o$

Let G he an abelian group and H g G ordg is finite Show th

Solution

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