Rank reduction of string C-group representations

2018/12/03 by Peter A. Brooksbank, Brooksbank, Peter A., Dimitri Leemans +1
Computer Science · Mathematics · #20D06 #20F55 #52B11 #Algebraic structures and combinatorial models #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR)

paper · pdf · doi:10.48550/arxiv.1812.01055

openalex publication_date 2018/12/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that a rank reduction technique for string C-group representations first used 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 3≤ r≤ d. 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 \rm Alt(11)---the only known group having `rank gaps'---is perhaps more unusual than previously thought.

Related

• The ranks of alternating string C-groups
• A rank augmentation theorem for rank 3 string C-group representations of the symmetric groups
• On the ranks of string C-group representations for symplectic and orthogonal groups
• String C-group representations of alternating groups
• String C-groups as transitive subgroups of Sym(n)