On the generation of Coxeter groups and their alternating subgroups by involutions

Yu, Rupert W. T.

doi:10.1515/jgth-2018-0214

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2021

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“…As is well known, Sym(n) is the Coxeter group of type A n−1 , and so this raises the question of finding d k (G) for the other finite irreducible Coxeter groups. In fact, the case when k = 2 has already been settled by Yu in [10]. Our main result, which we now state, answers this question for Coxeter groups of types B n and D n , and 3 ≤ k ≤ n. (ii) If k is even, then d k (G) = 2.…”

Section: Introductionmentioning

confidence: 52%

Generating finite Coxeter groups with elements of the same order

HART,

KELSEY,

ROWLEY

2021

Turk J Math

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Supposing G is a group and k a natural number, d k (G) is defined to be the minimal number of elements of G of order k which generate G (setting d k (G) = 0 if G has no such generating sets). This paper investigates d k (G) when G is a finite Coxeter group either of type B n or D n , or of exceptional type. Together with the work of Garzoni and Yu, this determines d k (G) for all finite irreducible Coxeter groups G when 2 ≤ k ≤ rank(G) (rank(G) + 1 when G is of type A n ).

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Section: Introductionmentioning

confidence: 52%