For each almost simple group G such that S≤ G≤ Aut (S) and S is a simple group of order
less than 900,000 listed in the Atlas of Finite Groups, we give, up to isomorphism, the …

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 …

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 …

We prove that if G is a string C-group of rank 4 and G≅ L 2 (q) with qa prime power, then q
must be 11 or 19. The polytopes arising are Grünbaum's 11-cell of type {3, 5, 3} for L 2 (11) …

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 …

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 …

Möbius Inversion in Suzuki Groups and Enumeration of Regular Objects | SpringerLink Skip to
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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 …

We determine, up to isomorphism and duality, the number of abstract regular polytopes of
rank three whose automorphism group is a Suzuki simple group Sz (q), with q an odd power …

For each d ≥ 3 d≥ 3, n ≥ 5 n≥ 5, and k_1, k_2, ..., k_ d-1 ≥ 2 k 1, k 2,…, kd-1≥ 2 with
k_1+ k_2+ ⋯+ k_ d-1 ≤ n-1 k 1+ k 2+⋯+ kd-1≤ n-1, we show how to construct a regular d …