2008/07/20 by Pedro Lopes, Lopes, Pedro
Computer Science · Mathematics · #05A05 #05A18 #20B15 #Advanced Topics in Algebra #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #math.CO #math.GR #msc:05A05 #msc:05A18 #msc:20B15
paper · pdf · doi:10.48550/arxiv.0807.3175
10 pages; version 2 accepted for publication in CEJM
openalex publication_date 2008/07/20 · arxiv created 2009/08/10 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.