7.10본 게시글은 현대대수학 바이블 교재 연습문제 7.10번에 대한 풀이입니다.Let $G$ be a group of order $155$ and $a, b$ be non-identity elements with distinct orders. Prove that the only subgroup of $G$ that contains $a, b$ is $G$ itself.Let $H$ be a subgroup of $G$ that contains $a, b$. Then, it should contain $, $.$|a|, |b|$ can only be only if $5, 31, 155$ by Lagrange's Theorem.Case 1)One of $|a|$ and $ |b|$ is $155$, say..