6 problems

Let a hereditary group property (HepGP) be a hereditary property of finite groups. Say that it is linearly atomic or strongly linearly atomic according to the corresponding atomici…

A hereditary group property (HepGP) is a group property closed under taking subgroups and isomorphisms. Two group properties are close when each is contained, up to the relevant as…

Let $\mathcal{G}_n$ be the space of marked $n$-generated groups, and let $S_n\subseteq\mathcal{G}_n$ be the set of simple groups, meaning groups in which the normal closure of ever…

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…