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math.GR2023★ 1 cited
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…
math.GR2023
On the maximal overgroups of Sylow subgroups of finite groups
Barbara Baumeister, Timothy C. Burness, Robert M. Guralnick +1
In this paper, we determine the finite groups with a Sylow -subgroup contained in a unique maximal subgroup. The proof involves a reduction to almost simple groups, and our main…