I dont understand the concept of $\Omega_1(P)$ of a $p$-group! I Know $\Omega_1(P)=\langle \lbrace x \in P | x^p=1 \rbrace \rangle$. For example if $P$ is non-cyclic such that $P$ has atleast one cyclic maximal subgroup, then what can say about $\Omega_1(P)$.
Please Hint me. Thanks.