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 unit group of finite semisimple group algebras of non-metabelian groups up to order 72

Gaurav Mittal, Rajendra Kumar Sharma (2021)

Mathematica Bohemica

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We characterize the unit group of semisimple group algebras $𝔽_{q} G$ of some non-metabelian groups, where $F_{q}$ is a field with $q = p^{k}$ elements for $p$ prime and a positive integer $k$ . In particular, we consider all 6 non-metabelian groups of order 48, the only non-metabelian group $((C_{3} \times C_{3}) ⋊ C_{3}) ⋊ C_{2}$ of order 54, and 7 non-metabelian groups of order 72. This completes the study of unit groups of semisimple group algebras for groups upto order 72.

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 ...

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 unit group of finite semisimple group algebras of non-metabelian groups up to order 72

On the Davenport constant and group algebras

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

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

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