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A direct factor theorem for commutative group algebras

William Ullery (1992)

Commentationes Mathematicae Universitatis Carolinae

Suppose $F$ is a field of characteristic $p \neq 0$ and $H$ is a $p$ -primary abelian $A$ -group. It is shown that $H$ is a direct factor of the group of units of the group algebra $F H$ .

A homological exact sequence associated with a family of normal subgroups

Antonio G. Rodicio (1987)

Cahiers de Topologie et Géométrie Différentielle Catégoriques

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 isomorphic commutative group algebras over certain rings.

Danchev, Peter (2005)

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

A note on normal generation and generation of groups

Andreas Thom (2015)

Communications in Mathematics

In this note we study sets of normal generators of finitely presented residually $p$ -finite groups. We show that if an infinite, finitely presented, residually $p$ -finite group $G$ is normally generated by $g_{1}, \dots, g_{k}$ with order $n_{1}, \dots, n_{k} \in {1, 2, \dots} \cup {\infty}$ , then $β_{1}^{(2)} (G) \leq k - 1 - \sum_{i = 1}^{k} \frac{1}{n_{i}},$ where $β_{1}^{(2)} (G)$ denotes the first $ℓ^{2}$ -Betti number of $G$ . We also show that any $k$ -generated group with $β_{1}^{(2)} (G) \geq k - 1 - ε$ must have girth greater than or equal $1 / ε$ .

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 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 three types of quasisymmetric functions.

Petersen, T. Kyle (2005)

The Electronic Journal of Combinatorics [electronic only]

A Note On Units And Divisors Of Zero In Group Rings

N. J. Groenewald, H. J. Schutte (1982)

Publications de l'Institut Mathématique

A semigroup approach to wreath-product extensions of Solomon's descent algebras.

Hsiao, Samuel K. (2009)

The Electronic Journal of Combinatorics [electronic only]

Abelian p-adic Group Rings.

Eugene Spiegel (1975)

Commentarii mathematici Helvetici

Algebras and Quaternion Defect Groups. I.

Karin Erdmann (1988)

Mathematische Annalen

Algebras and Quaternion Defect Groups. II.

Karin Erdmann (1988)

Mathematische Annalen

Almost Split Sequences over p-adic Rings.

J.A. Green, M.T.A.D. Nogueira (1988)

Mathematische Zeitschrift

An algorithm for the decomposition of ideals of the group ring of a symmetric group.

Fiedler, B. (1997)

Séminaire Lotharingien de Combinatoire [electronic only]

An analogue of the Duistermaat-van der Kallen theorem for group algebras

Wenhua Zhao, Roel Willems (2012)

Open Mathematics

Let G be a group, R an integral domain, and V G the R-subspace of the group algebra R[G] consisting of all the elements of R[G] whose coefficient of the identity element 1G of G is equal to zero. Motivated by the Mathieu conjecture [Mathieu O., Some conjectures about invariant theory and their applications, In: Algèbre non Commutative, Groupes Quantiques et Invariants, Reims, June 26–30, 1995, Sémin. Congr., 2, Société Mathématique de France, Paris, 1997, 263–279], the Duistermaat-van der Kallen...

Currently displaying 1 – 20 of 23