Huppert’s conjecture and almost simple groups
Rendiconti del Seminario Matematico della Università di Padova, Tome 148 (2022), pp. 173-184.
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Let G be a finite group and 𝖼𝖽(G) denote the set of complex irreducible character degrees of G. In this paper, we prove that if G is a finite group and H is an almost simple group whose socle is H 0 = PSL (2,q) with q=2 f (f prime) such that 𝖼𝖽(G)=𝖼𝖽(H), then there exists an abelian subgroup A of G such that G/A is isomorphic to H. In view of Huppert's conjecture (2000), the main result of this paper gives rise to some examples that G is not necessarily a direct product of A and H, and consequently, we cannot extend this conjecture to almost simple groups.

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DOI : 10.4171/rsmup/103
Classification : 20 
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     author = {Ashraf Daneshkhah},
     title = {Huppert{\textquoteright}s conjecture and almost simple groups},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     pages = {173--184},
     volume = {148},
     year = {2022},
     doi = {10.4171/rsmup/103},
     mrnumber = {4542376},
     zbl = {07673825},
     language = {en},
     url = {http://archive.numdam.org/articles/10.4171/rsmup/103/}
}
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Ashraf Daneshkhah. Huppert’s conjecture and almost simple groups. Rendiconti del Seminario Matematico della Università di Padova, Tome 148 (2022), pp. 173-184. doi : 10.4171/rsmup/103. http://archive.numdam.org/articles/10.4171/rsmup/103/

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