Conjugacy classes contained in normal subgroups: an overview
We survey known results concerning how the conjugacy classes contained in a normal subgroup and their sizes exert an influence on the normal structure of a finite group. The approach is mainly presented in the framework of graphs associated to the conjugacy classes, which have been introduced and de...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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University of Isfahan
2018-03-01
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| Series: | International Journal of Group Theory |
| Subjects: | |
| Online Access: | http://ijgt.ui.ac.ir/article_21216_521a00edf9dcb7b91295b2b081a9a468.pdf |
| Summary: | We survey known results concerning how the conjugacy classes contained in a normal subgroup and their sizes exert an influence on the normal structure of a finite group. The approach is mainly presented in the framework of graphs associated to the conjugacy classes, which have been introduced and developed in the past few years. We will see how the properties of these graphs, along with some extensions of the classic Landau's Theorem on conjugacy classes for normal subgroups, have been used in order to classify groups and normal subgroups satisfying certain conjugacy class numerical conditions. |
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| ISSN: | 2251-7650 2251-7669 |