Highest rank of a polytope for An. Issue 1 (28th April 2017)

• Record Type: Journal Article
• Authors: Cameron, Peter J.; Fernandes, Maria Elisa; Leemans, Dimitri; Mixer, Mark
• Is Part Of: Proceedings of the London Mathematical Society. Volume 115:Issue 1(2017)
• Page Start: 135
• Page End: 176
• Publication Date: 2017-04-28
• Subjects: 52B11 -- 20D06 (primary); Mathematics -- Periodicals; Mathematics; Periodicals; 510
• DOI: 10.1112/plms.12039
• Languages: English
• ISSNs: 0024-6115

Abstract

Abstract: We prove that the highest rank of a string C‐group constructed from an alternating group A n is 3 if n = 5, 4 if n = 9, 5 if n = 10, 6 if n = 11, and ⌊ ( n − 1 ) / 2 ⌋ if n ⩾ 12 . Moreover, if n = 3, 4, 6, 7, or 8, the group A n is not a string C‐group. This solves a conjecture made by the last three authors in 2012.