arXiv subjects

C. M. Scoppola

Publications and source records attributed to C. M. Scoppola.

3 recordsLinked to original sources

arXiv2025

The derangements subgroup in a finite permutation group and the Frobenius--Wielandt Theorem

It is known that if the derangements subgroup of a transitive non-regular permutation group is a proper subgroup, then it is a Frobenius--Wielandt kernel, and, conversely, minimal Frobenius--Wielandt kernels are proper derangements subgroups. We present here a short survey of the literature on this topic, and we show that, although there are no restrictions on the structure of the $p$-groups appearing as Frobenius--Wielandt complements, a $p$-group appears as a one-point stabiliser in a transitive non-regular permutation group with a proper derangements subgroup if and only if it satisfies a certain group-theoretic condition.

math.GR↗

arXiv2024

Elements of prime order in the upper central series of a group of prime-power order

We investigate the occurrence of elements of order $p$ in the upper central series of a finite $p$-group.

math.GR↗

arXiv2015

Finite morphic $p$-groups

According to Li, Nicholson and Zan, a group $G$ is said to be morphic if, for every pair $N_{1}, N_{2}$ of normal subgroups, each of the conditions $G/N_{1} \cong N_{2}$ and $G/N_{2} \cong N_{1}$ implies the other. Finite, homocyclic $p$-groups are morphic, and so is the nonabelian group of order $p^{3}$ and exponent $p$, for $p$ an odd prime. It follows from results of An, Ding and Zhan on self dual groups that these are the only examples of finite, morphic $p$-groups. In this paper we obtain the same result under a weaker hypotesis.

math.GR↗