Almost Engel finite and profinite groups

Almost Engel finite and profinite groups

Maximal Subgroups in Finite and Profinite Groups

We prove that if a finitely generated profinite group G is not generated with positive probability by finitely many random elements, then every finite group F is obtained as a quotient of an open subgroup of G. The proof involves the study of maximal subgroups of profinite groups, as well as techniques from finite permutation groups and finite Chevalley groups. Confirming a conjecture from Ann....

Engel-like Identities Characterizing Finite Solvable Groups

Engel-like Identities Characterising Finite Solvable Groups

Subgroups of Finite Index in Profinite Groups

One way to view Theorem 1.1 is as a statement that the algebraic structure of a finitely generated profinite group somehow also encodes the topological structure. That is, if one wishes to know the open subgroups of a profinite group G, a topological property, one must only consider the subgroups of G of finite index, an algebraic property. As profinite groups are compact topological spaces, an...