On locally finite $p$-groups satisfying an Engel condition

4-Engel Groups are Locally Nilpotent

Questions about nilpotency of groups satisfying Engel conditions have been considered since 1936, when Zorn proved that finite Engel groups are nilpotent. We prove that 4-Engel groups are locally nilpotent. Our proof makes substantial use of both hand and machine calculations.

Outer Automorphisms of Locally Finite p-Groups∗

Every group is an outer automorphism group of a locally finite p-group. This extends an earlier result [3] about countable outer automorphism groups. It is also in sharp contrast to results concerning the existence of outer automorphisms of nilpotent groups in [6, 13, 14].

Engel-like Identities Characterizing Finite Solvable Groups

Engel-like Identities Characterising Finite Solvable Groups

Almost Engel finite and profinite groups