Extraspecially Irreducible Groups
R. Dark, A.D. Feldman, M.D. Pérez-Ramos
Advances in Group Theory and Applications · 2016
doi:10.4399/97888548970144 (opens in a new tab)
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Abstract
Given distinct prime numbers $q$ and $r$, we construct a semidirect product $CR$ with $R\vartriangleleft CR$, where $C$ is a cyclic group of order $q$, and $R$ is an extraspecial $r$-group, such that $C$ centralizes $R'$, and $R$ is minimal among the extraspecial normal subgroups of $CR$. We also calculate the automorphism group of $CR$, and we investigate certain situations in which an automorphism fixes a nontrivial element of $R/R'$.
Abstract licence: CC BY-NC
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