Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8896148 | Journal of Algebra | 2018 | 40 Pages |
Abstract
A transitive permutation group is semiprimitive if each of its normal subgroups is transitive or semiregular. Interest in this class of groups is motivated by two sources: problems arising in universal algebra related to collapsing monoids and the graph-restrictive problem for permutation groups. Here we develop a theory of semiprimitive groups which encompasses their structure, their quotient actions and a method by which all finite semiprimitive groups are constructed. We also extend some results from the theory of primitive groups to semiprimitive groups, and conclude with open problems of a similar nature.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Michael Giudici, Luke Morgan,