A theory of semiprimitive groups

Research output: Contribution to journalArticle

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.

LanguageEnglish
Pages146-185
Number of pages40
JournalJournal of Algebra
Volume503
DOIs
StatePublished - 1 Jun 2018

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Permutation group
Primitive Group
Semiregular
Universal Algebra
Collapsing
Monoids
Normal subgroup
Open Problems
Quotient
Finite Group
Graph in graph theory
Class

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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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A theory of semiprimitive groups. / Giudici, Michael; Morgan, Luke.

In: Journal of Algebra, Vol. 503, 01.06.2018, p. 146-185.

Research output: Contribution to journalArticle

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