Vladimir V. Kirichenko, Leonid A. Kurdachenko, Igor Ya. Subbotin, “Some related to pronormality subgroup families and the properties of a group”, Algebra Discrete Math., 2011, Volume 11, Issue 1,Pages <nobr>75

This article is cited in 5 papers

SURVEY ARTICLE

Some related to pronormality subgroup families and the properties of a group

Vladimir V. Kirichenko^a, Leonid A. Kurdachenko^b, Igor Ya. Subbotin^c

^a Department of Geometry, School of Mechanics and Mathematics, Kyiv National Taras Shevchenko University, Volodymyrska, 64, Kyiv, 01033, Ukraine
^b Department of Algebra, School of Mathematics and Mechanics, National University of Dnepropetrovsk, Gagarin Prospect 72, Dnepropetrovsk 10, 49010, Ukraine
^c Department of Mathematics and Natural Sciences, National University, 5245 Pacific Concourse Drive, Los Angeles, CA 90045-6904, USA

Abstract: Some influential families of subgroups such as pronormal subgroups, contranormal subgroups, and abnormal subgroups, their generalizations, characterizations, interplays between them and the group, and their connections to other types of subgroups have been considered.

Keywords: normal subgroups, subnormal subgroup, contranormal subgroup, abnormal subgroups, pronormal subgroups, transitivity of normality, permutable subgroups, soluble group, radical group, locally graded group.

MSC: 20E15, 20E34, 20F19, 20F22

Received: 14.03.2011
Revised: 18.03.2011

Language: English