TY - JOUR
T1 - Almost central involutions in split extensions of Coxeter groups by graph automorphisms
AU - Nuida, Koji
N1 - Funding Information:
Acknowledgement. This paper is part of the author’s dissertation [17]. The author would like to express his deep gratitude to every one who helped him, especially to his supervisor Itaru Terada, and also to Kazuhiko Koike, for their valuable advice and encouragement. The author was supported by JSPS Research Fellowship throughout this research.
PY - 2007/3/20
Y1 - 2007/3/20
N2 - Given a split extension W ⋊ G, where W is an arbitrary Coxeter group and G a group of automorphisms of the Coxeter graph of W, we determine all involutions in W ⋊ G whose centralizers are of finite index. Our result has applications to many problems such as the isomorphism problem for general Coxeter groups. In the course of the proof, some properties of certain special elements and of fixed-point subgroups of graph automorphisms in Coxeter groups which are of independent interest are given.
AB - Given a split extension W ⋊ G, where W is an arbitrary Coxeter group and G a group of automorphisms of the Coxeter graph of W, we determine all involutions in W ⋊ G whose centralizers are of finite index. Our result has applications to many problems such as the isomorphism problem for general Coxeter groups. In the course of the proof, some properties of certain special elements and of fixed-point subgroups of graph automorphisms in Coxeter groups which are of independent interest are given.
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U2 - 10.1515/JGT.2007.011
DO - 10.1515/JGT.2007.011
M3 - Article
AN - SCOPUS:34247529896
SN - 1433-5883
VL - 10
SP - 139
EP - 166
JO - Journal of Group Theory
JF - Journal of Group Theory
IS - 2
ER -