Nicholas J. Werner

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math.GR2024

Exponential and weakly exponential subgroups of finite groups

Eric Swartz, Nicholas J. Werner

Sabatini (2024) defined a subgroup $H$ of $G$ to be an exponential subgroup if $x^{∣ G : H ∣} \in H$ for all $x \in G$ . Exponential subgroups are a generalization of normal (and subnor…

math.GR2024

A Note on Finite Nilpotent Groups

Nicholas J. Werner

It is well known that if $G$ is a group and $H$ is a normal subgroup of $G$ of finite index $k$ , then $x^{k} \in H$ for every $x \in G$ . We examine finite groups $G$ with the propert…