University of Sydney Algebra Seminar

Maria Elisa Fernandes (University of Aveiro)

Friday 12 Feb, 12-1pm, Place: New Law School Lecture Theatre 026

Highest rank of a polytope for \(A_n\)

The existence of a regular polytope with a given automorphism group G can be translated into a group-theoretic condition on a generating set of involutions for G. For G the symmetric group \(S_n\), the maximum rank of such a polytope is n-1, with equality only for the regular simplex. We prove that the highest rank of a string C-group constructed from an alternating group \(A_n\) is 0 if n=3, 4, 6, 7, 8; 3 if n=5; 4 if n=9; 5 if n=10; 6 if n=11; and \(\lfloor(n-1)/2\rfloor\) if \(n >11\).