Permutations which make transitive groups primitive

• Autorzy: Pedro Lopes
• Języki publikacji: EN

Abstrakty

EN

In this article we look into characterizing primitive groups in the following way. Given a primitive group we single out a subset of its generators such that these generators alone (the so-called primitive generators) imply the group is primitive. The remaining generators ensure transitivity or comply with specific features of the group. We show that, other than the symmetric and alternating groups, there are infinitely many primitive groups with one primitive generator each. These primitive groups are certain Mathieu groups, certain projective general and projective special linear groups, and certain subgroups of some affine special linear groups.

Słowa kluczowe

EN

Primitive groups; Permutations; Partitions

Kategorie tematyczne

• 05A05: Permutations, words, matrices
• 05A18: Partitions of sets
• 20B15: Primitive groups

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2009
• Tom: 7
• Numer: 4
• Strony: 650-659

Daty

wydano

2009-12-01

online

2009-10-31

Twórcy

autor

Pedro Lopes

• Department of Mathematics, Instituto Superior Técnico, Technical University of Lisbon, Lisbon, Portugal

Bibliografia

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Identyfikatory

DOI

10.2478/s11533-009-0050-3