We prove that a finite group in which any two nontrivial p-elements are conjugate have Sylow p-subgroups which are either elementary abelian or extra-special of order p 3 and exponent p.
No takes yet. Share an insight, caveat, or question.
Külshammer et al. (2014) studied this question.
Synapse has enriched one closely related paper. Consider it for comparative context: