Surjective word maps and Burnside's p^a q^b theorem

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Title: Surjective word maps and Burnside's p^a q^b theorem
Authors: Liebeck, MW
Guralnick, R
O'Brien, E
Shalev, A
Tiep, PH
Item Type: Journal Article
Abstract: We prove surjectivity of certain word maps on finite non-abelian simple groups. More precisely, we prove the following: if N is a product of two prime powers, then the word map (x,y)↦xNyN is surjective on every finite non-abelian simple group; if N is an odd integer, then the word map (x,y,z)↦xNyNzN is surjective on every finite quasisimple group. These generalize classical theorems of Burnside and Feit–Thompson. We also prove asymptotic results about the surjectivity of the word map (x,y)↦xNyN that depend on the number of prime factors of the integer N.
Issue Date: 1-Aug-2018
Date of Acceptance: 8-Feb-2018
URI: http://hdl.handle.net/10044/1/57240
DOI: https://dx.doi.org/10.1007/s00222-018-0795-z
ISSN: 0020-9910
Publisher: Springer Verlag
Start Page: 589
End Page: 695
Journal / Book Title: Inventiones Mathematicae
Volume: 213
Issue: 2
Copyright Statement: © Springer-Verlag GmbH Germany, part of Springer Nature 2018. The final publication is available at Springer via https://link.springer.com/article/10.1007%2Fs00222-018-0795-z
Keywords: Science & Technology
Physical Sciences
Mathematics
FINITE SIMPLE-GROUPS
CONJUGACY CLASSES
LIE TYPE
EXCEPTIONAL GROUPS
CLASSICAL-GROUPS
UNIPOTENT CHARACTERS
ORTHOGONAL GROUPS
CHEVALLEY-GROUPS
WARING PROBLEM
LINEAR-GROUPS
0101 Pure Mathematics
General Mathematics
Publication Status: Published
Online Publication Date: 2018-03-01
Appears in Collections:Pure Mathematics
Mathematics
Faculty of Natural Sciences



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