Locally inner automorphisms of CC-groups

Central-by-Chernikov groups are compact co-Chernikov CC-groups

“…In this paper we first establish that G is always a normal CC-central subgroup of L (Theorem 1 below) and so a natural question arises: characterize those G for which L itself is a CC-group. The answer will be given in the main results of this paper, which provide full characterizations and some features of the group of locally inner automorphisms of G then completing previous results of [7].…”

“…In the same way, in some papers like [1], [5], [6] or [7], a similar theory has been developed for CC-groups, a natural extension of the concept of an FC-group. By definition (Polovicky [9] but see also [10,Theorem 4.36]), an element x of a group G is said to be a CC-element of G if G/C G (x G ) is a Chernikov group.…”

“…We finally show that α is surjective so that φ will be the required isomorphism. Let θ ∈ Linn G. If X is a finite subset of G, by Lemma (2.1) of [7], there is some element g ∈ G such that h θ = h g for all h ∈ X G . Then…”

“…The pro-Chernikov completion of (G/Z, C) was calculated in the Theorem (2.3) of [7]. This is the group of locally inner automorphisms Linn G of G, which is a co-Chernikov group relative to the system K = {C Linn G (X G ) | X is a finite subset of G}.…”

Countable periodic CC-groups as automorphism groups

“…By Lemma 1, G is a CC-group and G/Z is periodic. Since AutG is countable, Theorem 4.5 of [6] shows that G/Z is a Cernikov group. Let D/Z be the divisible radical of G/Z.…”