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arXiv · 1607.03798

A theory of semiprimitive groups

Michael Giudici·Luke Morgan
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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.

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Michael Giudici, Luke Morgan. 2016-07-13. A theory of semiprimitive groups. https://arxiv.org/abs/1607.03798

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