Group Theory 07/29/2017 by Yu · Published 07/29/2017 The Normalizer of a Proper Subgroup of a Nilpotent Group is Strictly Bigger Problem 523 Let $G$ be a nilpotent group and let $H$ be a proper subgroup of $G$. Then prove that $H \subsetneq N_G(H)$, where $N_G(H)$ is the normalizer of $H$ in $G$. Read solution Click here if solved 37 Add to solve later

Group Theory 09/30/2016 by Yu · Published 09/30/2016 · Last modified 07/29/2017 If a Subgroup $H$ is in the Center of a Group $G$ and $G/H$ is Nilpotent, then $G$ is Nilpotent Problem 128 Let $G$ be a nilpotent group and let $H$ be a subgroup such that $H$ is a subgroup in the center $Z(G)$ of $G$. Suppose that the quotient $G/H$ is nilpotent. Then show that $G$ is also nilpotent. Read solution Click here if solved 18 Add to solve later