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Subjects
20-XX Group theory and generalizations
20Dxx Abstract finite groups
20D60 Arithmetic and combinatorial problems

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Displaying 21 – 23 of 23

The symmetric group of degree six can be covered by 13 and no fewer proper subgroups.

Abdollahi, A., Ashraf, F., Shaker, S.M. (2007)

Bulletin of the Malaysian Mathematical Sciences Society. Second Series

The weights of irreducible ${SL}_{3} (q)$ -modules in the defining characteristic.

Zavarnitsine, A.V. (2004)

Sibirskij Matematicheskij Zhurnal

Thompson’s conjecture for the alternating group of degree $2 p$ and $2 p + 1$

Azam Babai, Ali Mahmoudifar (2017)

Czechoslovak Mathematical Journal

For a finite group $G$ denote by $N (G)$ the set of conjugacy class sizes of $G$ . In 1980s, J. G. Thompson posed the following conjecture: If $L$ is a finite nonabelian simple group, $G$ is a finite group with trivial center and $N (G) = N (L)$ , then $G ≅ L$ . We prove this conjecture for an infinite class of simple groups. Let $p$ be an odd prime. We show that every finite group $G$ with the property $Z (G) = 1$ and $N (G) = N (A_{i})$ is necessarily isomorphic to $A_{i}$ , where $i \in {2 p, 2 p + 1}$ .

Currently displaying 21 – 23 of 23

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