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math.GR2024
Counting in nilpotent injectors and Carter subgroups
Stefanos Aivazidis, Maria Loukaki, John Shareshian
We investigate number-theoretic properties of the collection of nilpotent injectors or nilpotent projectors containing certain subgroups of finite soluble (or -constr…
math.GR2024
Invariable generation of finite simple groups and rational homology of coset posets
Robert M. Guralnick, John Shareshian, Russ Woodroofe
We show that every finite simple group is generated invariably by a Sylow subgroup and a cyclic group. It follows that that the order complex of the coset poset of an arbitrary fin…