Publication Date

12-2019

Description

We show that a rank reduction technique for string C-group representations first used in [Adv. Math. 228 (2018), pp. 3207–3222] for the symmetric groups generalizes to arbitrary settings. The technique permits us, among other things, to prove that orthogonal groups defined on d-dimensional modules over fields of even order greater than 2 possess string C-group representations of all ranks. The broad applicability of the rank reduction technique provides fresh impetus to construct, for suitable families of groups, string C-groups of highest possible rank. It also suggests that the alternating group Alt(11)—the only known group having “rank gaps”—is perhaps more unusual than previously thought.

Journal

Proceedings of the American Mathematical Society

Volume

147

Issue

12

First Page

5421

Last Page

5426

Department

Mathematics

Comments

Author's Accepted Manuscript

© 2020 Peter A. Brooksbank, CC-BY-NC

First published in Proceedings of the American Mathematical Society in 2020, published by the American Mathematical Society

Also available on arXiv.org https://arxiv.org/pdf/1812.01055.pdf

Open Access

Full text attached

DOI

https://doi.org/10.1090/proc/14666

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