Enumeration of conjugacy classes in affine groups

Jason Fulman, Robert M. Guralnick

Type: Article

Publication Date: 2024-04-30

Citations: 0

DOI: https://doi.org/10.2140/ant.2024.18.1189

Abstract

We study the conjugacy classes of the classical affine groups.We derive generating functions for the number of classes analogous to formulas of Wall and the authors for the classical groups.We use these to get good upper bounds for the number of classes.These naturally come up as difficult cases in the study of the non-coprime k(GV ) problem of Brauer.

Locations

Algebra & Number Theory - View - PDF
arXiv (Cornell University) - View - PDF

Similar Works

Action	Title	Year	Authors
+	Enumeration of conjugacy classes in affine groups	2021	Jason Fulman Robert M. Guralnick
+	Counting Real Conjugacy Classes in Some Finite Classical Groups	2018	Elena Amparo
+	Fixed conjugacy classes of normal subgroups and the k(GV)-problem	2005	Thomas Michael Keller
+ PDF Chat	CONJUGACY CLASSES IN CLASSICAL GROUPS	1983	Takashi Iwamoto
+	Counting conjugacy classes for unitriangular matrices	2015	Antonio Vera López María Asunción García Sánchez
+	The non-coprime <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:mi>k</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi mathvariant="italic">GV</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math> problem	2005	Robert M. Guralnick Pham Huu Tiep
+	Fixed conjugacy classes of normal subgroups and the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:mi>k</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>G</mml:mi><mml:mi>V</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math>-problem	2005	Thomas Michael Keller
+ PDF Chat	Book Review: Conjugacy classes in algebraic groups	1975	Andy R. Magid
+	Conjugacy Class Sizes in Affine Semi-linear Groups	2020	Hossein Shahrtash
+	A combinatorial approach to the conjugacy classes of Mathieu simple groups	1996	正人沢辺
+ PDF Chat	The geometry of conjugation in affine Coxeter groups	2024	Elizabeth Milićević Petra Schwer Anne Thomas
+	The Number of Conjugacy Classes	1998	M. Reid
+	Counting conjugacy classes of unitriangular groups associated to finite-dimensional algebras	1998	Geoffrey R. Robinson
+	Virtual Artin groups	2021	Paolo Bellingeri Luis Paris Anne‐Laure Thiel
+	Virtual Artin groups	2021	Paolo Bellingeri Luis Paris Anne‐Laure Thiel
+	Poincaré series of subsets of affine Weyl groups	2008	Sankaran Viswanath
+	A note on the parametrization of conjugacy classes	1972	R.W Carter Gordon Bradley Elkington
+	Poincare series of subsets of affine Weyl groups	2006	Sankaran Viswanath
+ PDF Chat	Unipotent class representatives for finite classical groups	2016	Samuel Gonshaw Martin W. Liebeck E. A. O’Brien
+	Conjugacy in finite classical groups	2024	Giovanni De Franceschi Martin W. Liebeck E. A. O’Brien

Works That Cite This (0)

Action	Title	Year	Authors

Works Cited by This (12)

Action	Title	Year	Authors
+	Unipotent and Nilpotent Classes in Simple Algebraic Groups and Lie Algebras	2012	Martin W. Liebeck Gary M. Seitz
+	Fixed conjugacy classes of normal subgroups and the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:mi>k</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>G</mml:mi><mml:mi>V</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math>-problem	2005	Thomas Michael Keller
+ PDF Chat	Numbers of conjugacy classes in some finite classical groups	1981	I. G. Macdonald
+ PDF Chat	The Characters of a Maximal Parabolic Subgroup of $GL_n(\mathbf{F}_q)$	1990	Yasumasa NAKADA Ken-ichi Shinoda
+	The Solution of the k(GV) Problem	2007	Peter Schmid
+ PDF Chat	Bounds on the number and sizes of conjugacy classes in finite Chevalley groups with applications to derangements	2012	Jason Fulman Robert M. Guralnick
+	ENCYCLOPEDIA OF MATHEMATICS AND ITS APPLICATIONS	1986	Neil White
+ PDF Chat	On the conjugacy classes in the unitary, symplectic and orthogonal groups	1963	G. E. Wall
+	Bounding numbers and heights of characters in p-constrained groups	2004	Geoffrey R. Robinson
+	The non-coprime <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:mi>k</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi mathvariant="italic">GV</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math> problem	2005	Robert M. Guralnick Pham Huu Tiep