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OD-characterization of almost simple groups related to L 2 ( 49 )

Liang Cai Zhang, Wu Jie Shi (2008)

Archivum Mathematicum

In the present paper, we classify groups with the same order and degree pattern as an almost simple group related to the projective special linear simple group L 2 ( 49 ) . As a consequence of this result we can give a positive answer to a conjecture of W. J. Shi and J. X. Bi, for all almost simple groups related to L 2 ( 49 ) except L 2 ( 49 ) · 2 2 . Also, we prove that if M is an almost simple group related to L 2 ( 49 ) except L 2 ( 49 ) · 2 2 and G is a finite group such that | G | = | M | and Γ ( G ) = Γ ( M ) , then G M .

On a group-theoretical generalization of the Gauss formula

Georgiana Fasolă, Marius Tărnăuceanu (2023)

Czechoslovak Mathematical Journal

We discuss a group-theoretical generalization of the well-known Gauss formula involving the function that counts the number of automorphisms of a finite group. This gives several characterizations of finite cyclic groups.

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