# Huppert's Conjecture for $Fi_{23}$

• ### Seyed Hassan Alavi

The University of Western Australia, Crawley,Australia
• ### Ashraf Daneshkhah

Bu-Ali Sina University, Hamedan, Iran
• ### H.P. Tong-Viet

University of KwaZulu-Natal, Pietermaritzburg, South Africa
• ### Thomas P. Wakefield

Youngstown State University, USA ## Abstract

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 $Fi_{23}$.

Seyed Hassan Alavi, Ashraf Daneshkhah, H.P. Tong-Viet, Thomas P. Wakefield, Huppert's Conjecture for $Fi_{23}$. Rend. Sem. Mat. Univ. Padova 126 (2011), pp. 201–211
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