Almost layer-finite groups and their characterizations

V. Senashov

A group is said to be layer-finite if it has finitely many elements of each order. This notion was first introduced by S. N. Chernikov in [1]. The layer-finite groups were studied by S. N. Chernikov, R. Baer, Kh. Kh. Mukhamedzhan, Ya. D. Polovitsky, et al. A detailed presentation of the theory of such groups is given in the monographs [2,3].

An almost layer-finite group is a group that is an extension of a layer-finite group by a finite group.

The author discovered new properties of almost layer-finite groups. In this talk, many examples of groups will be presented that distinguish between almost layer-finite groups and classes of groups that have close properties. An overview of characterizations of almost layer-finite groups in other classes of groups will be given.

References

1. S. N. Chernikov, On the theory of infinite \(p\)-groups, Doklady Akad. Nauk SSSR, 50 (1945), 71–72. (Russian)
2. S. N. Chernikov, Groups with given properties of a system of subgroups, "Nauka", Moscow (1980), 384 p. (Russian)
3. V. I. Senashov, Layer-finite groups. "Nauka", Novosibirsk (1993), 159 p. (Russian)

See also the author's pdf version (in Russian):