GL_n(\mathbbF_q)-analogues of some properties of n-cycles in \mathfrakS_n

2024/07/29 by Joel Brewster Lewis, Lewis, Joel Brewster
Computer Science · Mathematics · #Advanced Algebra and Geometry #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR)

paper · pdf · doi:10.48550/arxiv.2407.20347

openalex publication_date 2024/07/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give analogues in the finite general linear group of two elementary results concerning long cycles and transpositions in the symmetric group: first, that the long cycles are precisely the elements whose minimum-length factorizations into transpositions yield a generating set, and second, that a long cycle together with an appropriate transposition generates the whole symmetric group.

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