Scott Harper

activity

20232026

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3 papers · 1 filter

math.GR2024

Kronecker classes, normal coverings and chief factors of groups

Marco Fusari, Scott Harper, Pablo Spiga

For a group $G$ , a subgroup $U \leq G$ and a group $Inn (G) \leq A \leq Aut (G)$ , we say that $U$ is an $A$ -covering group of $G$ if $G = ⋃_{a \in A} U^{a}$ . A th…

math.GR2024

Derangements in intransitive groups

David Ellis, Scott Harper

Let $G$ be a nontrivial permutation group of degree $n$ . If $G$ is transitive, then a theorem of Jordan states that $G$ has a derangement. Equivalently, a finite group is never the…

math.GR2024

Representations of extensions of simple groups

Scott Harper, Martin W. Liebeck

Feit and Tits (1978) proved that a nontrivial projective representation of minimal dimension of a finite extension of a finite nonabelian simple group $G$ factors through a project…