Communications of the
Korean Mathematical Society CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024
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Commun. Korean Math. Soc. 2024; 39(2): 279-302

Online first article April 23, 2024      Printed April 30, 2024

https://doi.org/10.4134/CKMS.c230058

Copyright © The Korean Mathematical Society.

A survey of lengths of linear groups with respect to certain generating sets

Nguyen Thi Thai Ha

University of Transport and Communications

Abstract

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In this paper, we summarise and present results on involution lengths and commutator lengths of certain linear groups such as special linear groups, projective linear groups, upper triangle matrix groups and Vershik-Kerov groups. Some open problems motivated by these results are also proposed.

Keywords: Matrix decomposition, linear groups, involution length, commutator length

MSC numbers: Primary 15A23, 15B33, 15B36, 15B99

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