Pronormality and permutability in periodic FC--groups

N.A.Turbay

In this paper we study periodic locally soluble $FC$--groups in which permutability is a transitive relation and the class of groups in which all finite normal subgroups of Sylow subgroups are pronormal. The choice of class of periodic $FC$-groups is made, because it has sufficiently developed structure and is similar to the class of finite groups.

1. Beidleman J.C., Brewster B., Robinson D.J.S., Criteria for permutability to be transitive infinite groups, J. Algebra 222 (1999), 400--412.

2. Gorenstein D., Finite groups, Harper and Row, New York, 1968.

3. Robinson D.J.S., A course in the theory of groups, Springer, New York, 1982.

4. Schmidt R., Subgroups lattices of groups, Walter de Gruyter, Berlin, 1994.

5. Tomkinson M.J., FC-groups, Pitman, Boston, 1984.

6. G. Zacher, I gruppi risolubili finite in cui i sottogruppi di composizione coincidono con i sottogruppi quasi - normali, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. 37 (1964), no. 8, 150--154.

7. Турбай Н. А. Характеризация FC-групп, в которых условие переставляемости транзитивно // Вiсник Дніпропетр. ун-ту. Maтематика (2007), № 12.

8. Цыба Н.А. FC-группы, в которых условие переставляемости транзитивно // Вiсник Дніпропетр. ун-ту. Maтематика (2006), №11, 104--109.

	Pronormality and permutability in periodic FC--groups
Author	N.A.Turbay Department of Mathematics,Dnipropetrovsk National University, V. Naukova 13, Dnipropetrovsk 49050, Ukraine
Abstract	In this paper we study periodic locally soluble $FC$--groups in which permutability is a transitive relation and the class of groups in which all finite normal subgroups of Sylow subgroups are pronormal. The choice of class of periodic $FC$-groups is made, because it has sufficiently developed structure and is similar to the class of finite groups.
Keywords	pronormality, permutability, periodic FC-group
DOI	doi:10.30970/ms.29.2.132-138
Reference	1. Beidleman J.C., Brewster B., Robinson D.J.S., Criteria for permutability to be transitive infinite groups, J. Algebra 222 (1999), 400--412. 2. Gorenstein D., Finite groups, Harper and Row, New York, 1968. 3. Robinson D.J.S., A course in the theory of groups, Springer, New York, 1982. 4. Schmidt R., Subgroups lattices of groups, Walter de Gruyter, Berlin, 1994. 5. Tomkinson M.J., FC-groups, Pitman, Boston, 1984. 6. G. Zacher, I gruppi risolubili finite in cui i sottogruppi di composizione coincidono con i sottogruppi quasi - normali, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. 37 (1964), no. 8, 150--154. 7. Турбай Н. А. Характеризация FC-групп, в которых условие переставляемости транзитивно // Вiсник Дніпропетр. ун-ту. Maтематика (2007), № 12. 8. Цыба Н.А. FC-группы, в которых условие переставляемости транзитивно // Вiсник Дніпропетр. ун-ту. Maтематика (2006), №11, 104--109.
Pages	132-138
Volume	29
Issue	2
Year	2008
Journal	Matematychni Studii
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