Permutations Which Make Transitive Groups Primitive

Details Permutations Which Make Transitive Groups Primitive Permutations Which Make Transitive Groups Primitive

2008-07-20

arxiv.org/abs/0807.3175v2

Mathematics

Combinatorics

10 pages; version 2 accepted for publication in CEJM

Scientific paper

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.

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