Rendiconti del Seminario Matematico della Università di Padova

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Volume 126, 2011, pp. 201–211
DOI: 10.4171/RSMUP/126-11

Published online: 2011-12-31

Huppert's Conjecture for $Fi_{23}$

Seyed Hassan Alavi[1], Ashraf Daneshkhah[2], H.P. Tong-Viet[3] and T.P. Wakefield[4]

(1) The University of Western Australia, Crawley,Australia
(2) Bu-Ali Sina University, Hamedan, Iran
(3) University of KwaZulu-Natal, Pietermaritzburg, South Africa
(4) Youngstown State University, USA

Let $G$ denote a finite group and $\text{cd}(G)$ the set of irreducible character degrees of $G$. Bertram Huppert conjectured that if $H$ is a finite nonabelian simple group such that $\text{cd}(G) =\text{cd}(H)$, then $G\cong H \times A$, where $A$ is an abelian group. Huppert verified the conjecture for many of the sporadic simple groups. We illustrate the arguments by presenting the verification of Huppert's Conjecture for $Fi_{23}$.

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Alavi Seyed Hassan, Daneshkhah Ashraf, Tong-Viet H.P., Wakefield T.P.: Huppert's Conjecture for $Fi_{23}$. Rend. Sem. Mat. Univ. Padova 126 (2011), 201-211. doi: 10.4171/RSMUP/126-11