Is this subset of group, a subgroup of it?

Asked Nov 17 '14 at 15:18

Active Nov 17 '14 at 17:05

Viewed 75 times

Suppose that $G$ is a finite group, $n = |G|$, and $X$ be a non-empty subset of $G$. Is it true that $$ H := \{ x_1 x_2 \dots x_n | x_i \in X \} $$ is a subgroub of $G$?

Edit: Since $n=|G|$ so $H$ has identity. But whether $H$ is closed under group's operation? Since $G$ is finite it solves the problem.

edited Nov 17 '14 at 16:58

asked Nov 17 '14 at 15:18

Human Learning

1,033

Why do you say "$n = |G|$ so $H$ has identity"? – Christopher Nov 17 '14 at 15:32
4

$X$ is not empty so it has an element, $x$, now $1=x^n \in X$ – Human Learning Nov 17 '14 at 15:34
Sorry about all wrong directions. Im very confused now. How did you prove that the inverse element is in H? That kills the problem. – FormerMath Nov 17 '14 at 16:38
1

Sorry! But I did not prove that! – Human Learning Nov 17 '14 at 16:41
1

This question was asked before, I gave an answer here. Where did you find this problem by the way? I am interested because I've only seen it here on Math.SE. – Mikko Korhonen Nov 17 '14 at 17:02
My friend asks me. I'm not sure from his resource for the problem. Thank for link! – Human Learning Nov 17 '14 at 17:33

Is this subset of group, a subgroup of it?

0 Answers0