3 problems

FSZ Sylow conjecture. $G$ is FSZ if and only if all of its Sylow subgroups are FSZ.

Let $G$ be a group. It has BVC if there are virtually cyclic subgroups $V_1,\ldots,V_n$ such that every virtually cyclic subgroup of $G$ is conjugate to a subgroup of some $V_i$. B…

Let ${\mathscr{G}}$ be a class of finite groups, and let ${\mathscr{G}}^c$ denote its complement among the finite groups. A class is (cf-)ISLE if it has the (core-free) ISLE closur…