### 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 |

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### Cite this

*Journal of Algebra*,

*503*, 146-185. https://doi.org/10.1016/j.jalgebra.2017.12.040

}

*Journal of Algebra*, vol. 503, pp. 146-185. https://doi.org/10.1016/j.jalgebra.2017.12.040

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

Research output: Contribution to journal › Article

TY - JOUR

T1 - A theory of semiprimitive groups

AU - Giudici, Michael

AU - Morgan, Luke

PY - 2018/6/1

Y1 - 2018/6/1

N2 - 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.

AB - 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.

KW - Arc-transitive graphs

KW - Permutation group

KW - Primitive groups

KW - Semiprimitive groups

UR - http://www.scopus.com/inward/record.url?scp=85044604259&partnerID=8YFLogxK

U2 - 10.1016/j.jalgebra.2017.12.040

DO - 10.1016/j.jalgebra.2017.12.040

M3 - Article

VL - 503

SP - 146

EP - 185

JO - Journal of Algebra

JF - Journal of Algebra

SN - 0021-8693

ER -