Affine transformations of finite vector spaces with large orders or few\n cycles

2013/06/06 by Simon D. Guest, Joy Morris, Guest, Simon +5
Computer Science · Engineering · Mathematics · #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1306.1368

openalex publication_date 2013/06/06 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28

Abstract

Let V be a d-dimensional vector space over a field of prime order p. We\nclassify the affine transformations of V of order at least p^d/4, and apply\nthis classification to determine the finite primitive permutation groups of\naffine type, and of degree n, that contain a permutation of order at least n/4.\nUsing this result we obtain a classification of finite primitive permutation\ngroups of affine type containing a permutation with at most four cycles.\n

Citations

• Approximate formulas for some functions of prime numbers
• On the maximum orders of elements of finite almost simple groups and\n primitive permutation groups

Related

• Permutation groups on countable vector spaces over prime fields
• Finite primitive permutation groups containing a permutation having at most four cycles
• Primitive permutation groups and derangements of prime power order
• Primitive permutation groups of finite Morley rank and affine type
• A classification of primitive permutation groups with finite stabilizers