论文标题
关于$ d $ -maximal $ p $ -groups i
A note on $d$-maximal $p$-groups I
论文作者
论文摘要
如果每个子组$ h <g $ $ d（h）<d（g）$，则有限的$ p $ -group $ g $为$ d $ -maximal，其中$ d（g）$表示$ g $的生成器数量最小为$ g $。当$ g $由某些组$ a $执行时，可以制定类似的定义。我们将B. kahn和T. Laffey的结果推广到后一种情况，并特别提供替代性的简短证明。此外，我们回答了Y. Berkovich的问题，内容涉及最小的非米特西环$ P $ -Groups。
A finite $p$-group $G$ is said to be $d$-maximal if $d(H)<d(G)$ for every subgroup $H<G$, where $d(G)$ denotes the minimal number of generators of $G$. A similar definition can be formulated when $G$ is acted on by some group $A$. We generalize results of B. Kahn and T. Laffey to the latter case, and give them in particular alternative short proofs. We answer moreover a question of Y. Berkovich about the minimal non-metacyclic $p$-groups.
