On w-maximal groups
Jon Gonzalez-Sanchez, Benjamin Klopsch

TL;DR
This paper investigates the properties and classifications of finite groups that are maximal with respect to a specific verbal subgroup defined by a word, focusing on their structure and hereditary properties.
Contribution
It introduces the concepts of w-maximal and hereditarily w-maximal groups and studies their structural properties and classifications.
Findings
Characterization of w-maximal groups
Conditions for hereditary w-maximality
Examples of such groups and their properties
Abstract
Let be a word, i.e. an element of the free group on generators . The verbal subgroup of a group is the subgroup generated by the set of all -values in . We say that a (finite) group is -maximal if for all proper subgroups of and that is hereditarily -maximal if every subgroup of is -maximal. In this text we study -maximal and hereditarily -maximal (finite) groups.
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Taxonomy
TopicsFinite Group Theory Research · Geometric and Algebraic Topology · Limits and Structures in Graph Theory
