arXiv subjects
Publications and source records attributed to John K. McVey.
The goal of the paper "A new graph over semi-direct products of groups" is to define a graph Γ(G) on a group G when G splits over a normal subgroup. We demonstrate herein that the graph is ill-defined. We also attempt to ascertain causes for the discrepancies.
Given a Mersenne prime $q$ and a positive even integer $e$, let $F$ and $E$ be the fields of orders $q$ and $q^e$ respectively. Let $C$ be a cyclic subgroup of $E^\times$ whose index in $E^\times$ is divisible only by primes dividing $q - 1$. We compute the character degrees of the group $C \rtimes {\rm Gal} (E/F)$ by using the Galois connection between the subfields of $E$ and the Galois group ${\rm Gal} (E/F)$.