Conjugacy classes and centralisers in wreath products. (November 2022)

• Record Type: Journal Article
• Authors: Bernhardt, Dominik; Niemeyer, Alice C.; Rober, Friedrich; Wollenhaupt, Lucas
• Is Part Of: Journal of symbolic computation. Volume 113(2022)
• Page Start: 97
• Page End: 125
• Publication Date: 2022-11
• Subjects: 20E22 -- 20E45 -- 20-08; Wreath products -- Centralisers -- Conjugacy classes -- Conjugacy problem -- Permutation groups -- Cycle decomposition; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2022.02.005
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: In analogy to the disjoint cycle decomposition in permutation groups, Ore and Specht define a decomposition of elements of the full monomial group and exploit this to describe conjugacy classes and centralisers of elements in the full monomial group. We generalise their results to wreath products whose base group need not be finite and whose top group acts faithfully on a finite set. We parameterise conjugacy classes and centralisers of elements in such wreath products explicitly. For finite wreath products, our approach yields efficient algorithms for finding conjugating elements, conjugacy classes, and centralisers.