Тип публикации: статья из журнала
Год издания: 2020
Идентификатор DOI: 10.31489/2020M4/136-142
Ключевые слова: group, layer-finiteness, bottom layer, thin layer-finite group, spectrum, periodic group, sylow subgroup, abelian group, quasi-cyclic group, complete group
Аннотация: We consider the problem of recognizing a group by its bottom layer. This problem is solved in the class of layer-finite groups. A group is layer-finite if it has a finite number of elements of every order. This concept was first introduced by S. N. Chernikov. It appeared in connection with the study of infinite locally finite p-groПоказать полностьюups in the case when the center of the group has a finite index. S. N. Chernikov described the structure of an arbitrary group in which there are only finite elements of each order and introduced the concept of layer-finite groups in 1948. Bottom layer of the group G is a set of its elements of prime order. If have information about the bottom layer of a group we can receive results about its recognizability by bottom layer. The paper presents the examples of groups that are recognizable, almost recognizable and unrecognizable by its bottom layer under additional conditions.
Журнал: BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS
Выпуск журнала: Vol. 100, Is. 4
Номера страниц: 136-142
ISSN журнала: 25187929
Место издания: KARAGANDA
Издатель: KARAGANDA STATE UNIV