Unit groups of group algebras of some small groups

Gaohua Tang; Yangjiang Wei; Yuanlin Li

Displaying similar documents to “Unit groups of group algebras of some small groups”

A note on group algebras of $p$ -primary abelian groups

William Ullery (1995)

Commentationes Mathematicae Universitatis Carolinae

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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.

Basic subgroups in modular abelian group algebras

Peter Vassilev Danchev (2007)

Czechoslovak Mathematical Journal

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Suppose $F$ is a perfect field of $c h a r F = p \neq 0$ and $G$ is an arbitrary abelian multiplicative group with a $p$ -basic subgroup $B$ and $p$ -component $G_{p}$ . Let $F G$ be the group algebra with normed group of all units $V (F G)$ and its Sylow $p$ -subgroup $S (F G)$ , and let $I_{p} (F G; B)$ be the nilradical of the relative augmentation ideal $I (F G; B)$ of $F G$ with respect to $B$ . The main results that motivate this article are that $1 + I_{p} (F G; B)$ is basic in $S (F G)$ , and $B (1 + I_{p} (F G; B))$ is $p$ -basic in $V (F G)$ provided $G$ is $p$ -mixed. These achievements extend in some way a result of N. Nachev (1996)...

On the Davenport constant and group algebras

Daniel Smertnig (2010)

Colloquium Mathematicae

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For a finite abelian group G and a splitting field K of G, let (G,K) denote the largest integer l ∈ ℕ for which there is a sequence $S = g ₁ \cdot . . . \cdot g_{l}$ over G such that $(X^{g ₁} - a ₁) \cdot . . . \cdot (X^{g_{l}} - a_{l}) \neq 0 \in K [G]$ for all $a ₁, . . ., a_{l} \in K^{\times}$ . If (G) denotes the Davenport constant of G, then there is the straightforward inequality (G) - 1 ≤ (G,K). Equality holds for a variety of groups, and a conjecture of W. Gao et al. states that equality holds for all groups. We offer further groups for which equality holds, but we also give the first examples of groups G for...

The $H S P$ -Classes of Archimedean $l$ -groups with Weak Unit

Bernhard Banaschewski, Anthony Hager (2010)

Annales de la faculté des sciences de Toulouse Mathématiques

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$W$ denotes the class of abstract algebras of the title (with homomorphisms preserving unit). The familiar $H, S,$ and $P$ from universal algebra are here meant in $W$ . $ℤ$ and $ℝ$ denote the integers and the reals, with unit 1, qua $W$ -objects. $V$ denotes a non-void finite set of positive integers. Let $𝒢 \subseteq W$ be non-void and not ${{0}}$ . We show ...

Homomorphisms from the unitary group to the general linear group over complex number field and applications

Chong-Guang Cao, Xian Zhang (2002)

Archivum Mathematicum

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Let $M_{n}$ be the multiplicative semigroup of all $n \times n$ complex matrices, and let $U_{n}$ and $G L_{n}$ be the $n$ –degree unitary group and general linear group over complex number field, respectively. We characterize group homomorphisms from $U_{n}$ to $G L_{m}$ when $n > m \geq 1$ or $n = m \geq 3$ , and thereby determine multiplicative homomorphisms from $U_{n}$ to $M_{m}$ when $n > m \geq 1$ or $n = m \geq 3$ . This generalize Hochwald’s result in [Lin. Alg. Appl. 212/213:339-351(1994)]: if $f : U_{n} \to M_{n}$ is a spectrum–preserving multiplicative homomorphism, then there exists a matrix $R$ in $G L_{n}$ such...

A duality theorem for Dieudonné displays

Eike Lau (2009)

Annales scientifiques de l'École Normale Supérieure

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We show that the Zink equivalence between $p$ -divisible groups and Dieudonné displays over a complete local ring with perfect residue field of characteristic $p$ is compatible with duality. The proof relies on a new explicit formula for the $p$ -divisible group associated to a Dieudonné display.

Displaying similar documents to “Unit groups of group algebras of some small groups”

A note on group algebras of p -primary abelian groups

Basic subgroups in modular abelian group algebras

On the Davenport constant and group algebras

The H S P -Classes of Archimedean l -groups with Weak Unit

Homomorphisms from the unitary group to the general linear group over complex number field and applications

A duality theorem for Dieudonné displays

A note on group algebras of $p$ -primary abelian groups

The $H S P$ -Classes of Archimedean $l$ -groups with Weak Unit