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 …

Using the correspondence between abstract regular polytopes and string C-groups, in a
recent paper ME Fernandes, D. Leemans, and M. Mixer, J. Combin. Theory Ser. A, 119 …

Up to isomorphism and duality, there are exactly two nondegenerate abstract regular
polytopes of rank greater than $ n-3$(one of rank $ n-1$ and one of rank $ n-2$) with …

If G is a transitive group of degree n having a string C-group of rank r≥(n+ 3)/2, then G is
necessarily the symmetric group S n. We prove that if n is large enough, up to isomorphism …

Our paper deals with the classification of abstract regular polytopes for almost simple groups
with socle PSL (2, q). We consider all almost simple groups PSL (2, q)≤ G≤ P Γ L (2, q) and …

In this paper, we prove that for any positive integers n, s, t such that n≥ 10, s, t≥ 2 and n-1≥
s+ t, there exists a regular polytope with Schläfli type {2 s, 2 t} and its automorphism group is …

The automorphism group of every abstract regular polytope of type {k1|⋯| km} is a smooth
finite quotient of the corresponding Coxeter group [k1,…, km] satisfying a particular condition …

arXiv:1810.12450v2 [math.GR] 4 Jan 2019 Page 1 arXiv:1810.12450v2 [math.GR] 4 Jan 2019
STRING C-GROUP REPRESENTATIONS OF ALTERNATING GROUPS MARIA ELISA …

This paper examines abstract regular polytopes whose automorphism group is the
projective special linear group PSL (4, F q). For q odd we show that polytopes of rank 4 exist …

In this paper, we consider how the O'Nan sporadic simple group acts as the automorphism
group of an abstract regular polytope. In particular, we prove that there is no regular …