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arXiv · 2312.16319

Invariable generation of finite simple groups and rational homology of coset posets

Robert M. Guralnick·John Shareshian·Russ Woodroofe
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Abstract

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 finite group has nontrivial reduced rational homology.

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Robert M. Guralnick, John Shareshian, Russ Woodroofe. 2024-06-30. Invariable generation of finite simple groups and rational homology of coset posets. https://doi.org/10.1016/j.jalgebra.2024.06.015

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