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We prove that an isomorphism between saturated fusion systems over the same finite p-group is detected on the elementary abelian subgroups of the hyperfocal subgroup if p is odd, and on the abelian subgroups of the hyperfocal subgroup of exponent at most 4 if p = 2. For odd p, this has implications for mod p group cohomology.
When studying subgroups of $Out(F_n)$, one often replaces a given subgroup $H$ with one of its finite index subgroups $H_0$ so that virtual properties of $H$ become actual properties of $H_0$. In many cases, the finite index subgroup is $H_0 = H cap
In a recent paper of the first author and I. M. Isaacs it was shown that if m = m(G) is the maximal order of an abelian subgroup of the finite group G, then |G| divides m! ([AI18, Thm. 5.2]). The purpose of this brief note is to improve on the m! bou
Motivated in part by representation theoretic questions, we prove that if G is a finite quasi-simple group, then there exists an elementary abelian subgroup of G that intersects every conjugacy class of involutions of G.
This is the fourth and last in a series of four papers (with research announcement posted on this arXiv) that develop a decomposition theory for subgroups of $text{Out}(F_n)$. In this paper we develop general ping-pong techniques for the action of $t
Suppose $mathcal{E}$ is a normal subsystem of a saturated fusion system $mathcal{F}$ over $S$. If $Xleq S$ is fully $mathcal{F}$-normalized, then Aschbacher defined a normal subsystem $N_{mathcal{E}}(X)$ of $N_{mathcal{F}}(X)$. In this short note we