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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 group algebras of $p$ -primary abelian groups

William Ullery (1995)

Commentationes Mathematicae Universitatis Carolinae

Suppose $p$ is a prime number and $R$ is a commutative ring with unity of characteristic 0 in which $p$ is not a unit. Assume that $G$ and $H$ are $p$ -primary abelian groups such that the respective group algebras $R G$ and $R H$ are $R$ -isomorphic. Under certain restrictions on the ideal structure of $R$ , it is shown that $G$ and $H$ are isomorphic.

A note on Harish-Chandra induction.

Meinholf Geck (1993)

Manuscripta mathematica

A note on isomorphic commutative group algebras over certain rings.

Danchev, Peter (2005)

Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică

A note on representations of the finite Heisenberg group and sums of greatest common divisors.

Grassberger, Johannes, Hörmann, Günther (2001)

Discrete Mathematics and Theoretical Computer Science. DMTCS [electronic only]

A note on semilocal group rings

Angelina Y. M. Chin (2002)

Czechoslovak Mathematical Journal

Let $R$ be an associative ring with identity and let $J (R)$ denote the Jacobson radical of $R$ . $R$ is said to be semilocal if $R / J (R)$ is Artinian. In this paper we give necessary and sufficient conditions for the group ring $R G$ , where $G$ is an abelian group, to be semilocal.

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 isomorphism of modular group algebras of $p$ -mixed Abelian groups with divisible $p$ -components.

Danchev, Peter (2006)

Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică

A note on the projective representations of finite groups

Dănuţ Marcu (1999)

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 one-box-shift morphism between Specht modules.

Künzer, Matthias (2000)

Electronic Research Announcements of the American Mathematical Society [electronic only]

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 proof of Ph. Hall's theorem on dimension subgroups

A. Grzegorek (1979)

Colloquium Mathematicae

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