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.
Original language | English |
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Pages (from-to) | 146-185 |
Number of pages | 40 |
Journal | Journal of Algebra |
Volume | 503 |
DOIs | |
Publication status | Published - 1 Jun 2018 |