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Let $G$ be a finite group and $p$ a prime number. We prove that if $G$ is a finite group of order $| PSL (2, p^{2}) |$ such that $G$ has an irreducible character of degree $p^{2}$ and we know that $G$ has no irreducible character $θ$ such that $2 p ∣ θ (1)$ , then $G$ is isomorphic to $PSL (2, p^{2})$ . As a consequence of our result we prove that $PSL (2, p^{2})$ is uniquely determined by the structure of its complex group algebra.

A note on finite groups with few values in a column of the character table

Mariagrazia Bianchi, David Chillag, Emanuele Pacifici (2006)

Rendiconti del Seminario Matematico della Università di Padova

A note on the converse of the Clifford's theorem and some consequences

G. Navarro (1987)

Rendiconti del Seminario Matematico della Università di Padova

A note on the subclass algebra.

Karlof, John (1980)

International Journal of Mathematics and Mathematical Sciences

A problem of Kollár and Larsen on finite linear groups and crepant resolutions

Robert Guralnick, Pham Tiep (2012)

Journal of the European Mathematical Society

The notion of age of elements of complex linear groups was introduced by M. Reid and is of importance in algebraic geometry, in particular in the study of crepant resolutions and of quotients of Calabi–Yau varieties. In this paper, we solve a problem raised by J. Kollár and M. Larsen on the structure of finite irreducible linear groups generated by elements of age $\leq 1$ . More generally, we bound the dimension of finite irreducible linear groups generated by elements of bounded deviation. As a consequence...

A remark on homogeneous sets in finite groups. (Eine Bemerkung über homogene Mengen in endlichen Gruppen.)

Kerber, Adalbert (1984)

Séminaire Lotharingien de Combinatoire [electronic only]

A remark on the irreducible characters and fake degrees of finite real reflection groups.

E.M. Opdam (1995)

Inventiones mathematicae

A solvability criterion for finite groups related to character degrees

Babak Miraali, Sajjad Mahmood Robati (2020)

Czechoslovak Mathematical Journal

Let $m > 1$ be a fixed positive integer. In this paper, we consider finite groups each of whose nonlinear character degrees has exactly $m$ prime divisors. We show that such groups are solvable whenever $m > 2$ . Moreover, we prove that if $G$ is a non-solvable group with this property, then $m = 2$ and $G$ is an extension of $A_{7}$ or $S_{7}$ by a solvable group.

In this article we prove an effective version of the classical Brauer’s Theorem for integer class functions on finite groups.

A $λ$ -ring Frobenius characteristic for $G ≀ S_{n}$ .

Mendes, Anthony, Remmel, Jeffrey, Wagner, Jennifer (2004)

The Electronic Journal of Combinatorics [electronic only]

Abelian Normal Subgroups of M-Groups.

I. Martin Isaacs (1983)

Mathematische Zeitschrift

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A characterization of characters which arise from ...-normalizers.

A Characterization of GL(2, 3) and SL(2,5) by the Degrees of their Representations.

A characterization of $L_{2} (2^{f})$ in terms of the number of character zeros.

A Frobenius formula for the characters of the Hecke algebras.

A Gel'fand model for a Weyl group of type $B_{n}$ .

A local method in group cohomology.

A new characterization for the simple group $PSL (2, p^{2})$ by order and some character degrees