The influence of arrangement of subgroups on the group structure. (English) Zbl 1395.20015
Summary: Investigation of groups satisfying certain related to arrangement of subgroups conditions allows algebraists to introduce and describe many important classes of groups. Most of these conditions are based on the fundamental notion of normality and built with the help of this concept different subgroup chains (series). Some of important results obtained on this way we will discuss in the current survey.
MSC:
| 20E15 | Chains and lattices of subgroups, subnormal subgroups |
| 20F19 | Generalizations of solvable and nilpotent groups |
| 20E34 | General structure theorems for groups |
| 20F14 | Derived series, central series, and generalizations for groups |
| 20F18 | Nilpotent groups |
Keywords:
arrangement of subgroups; abnormal subgroups; pronormal subgroups; criteria of nilpotency; transitivity of normalityReferences:
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