Group Theory 07/28/2017 by Yu · Published 07/28/2017 Elements of Finite Order of an Abelian Group form a Subgroup Problem 522 Let $G$ be an abelian group and let $H$ be the subset of $G$ consisting of all elements of $G$ of finite order. That is, \[H=\{ a\in G \mid \text{the order of $a$ is finite}\}.\] Prove that $H$ is a subgroup of $G$. Read solution Click here if solved 171 Add to solve later
Group Theory 10/28/2016 by Yu · Published 10/28/2016 · Last modified 07/29/2017 Finite Group and Subgroup Criteria Problem 160 Let $G$ be a finite group and let $H$ be a subset of $G$ such that for any $a,b \in H$, $ab\in H$. Then show that $H$ is a subgroup of $G$. Read solution Click here if solved 20 Add to solve later