# Unit groups of group algebras of some small groups

Gaohua Tang; Yangjiang Wei; Yuanlin Li

Czechoslovak Mathematical Journal (2014)

- Volume: 64, Issue: 1, page 149-157
- ISSN: 0011-4642

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topTang, Gaohua, Wei, Yangjiang, and Li, Yuanlin. "Unit groups of group algebras of some small groups." Czechoslovak Mathematical Journal 64.1 (2014): 149-157. <http://eudml.org/doc/262013>.

@article{Tang2014,

abstract = {Let $FG$ be a group algebra of a group $G$ over a field $F$ and $\{\mathcal \{U\}\}(FG)$ the unit group of $FG$. It is a classical question to determine the structure of the unit group of the group algebra of a finite group over a finite field. In this article, the structure of the unit group of the group algebra of the non-abelian group $G$ with order $21$ over any finite field of characteristic $3$ is established. We also characterize the structure of the unit group of $FA_4$ over any finite field of characteristic $3$ and the structure of the unit group of $FQ_\{12\}$ over any finite field of characteristic $2$, where $Q_\{12\}=\langle x, y; x^6=1, y^2=x^3, x^y=x^\{-1\} \rangle $.},

author = {Tang, Gaohua, Wei, Yangjiang, Li, Yuanlin},

journal = {Czechoslovak Mathematical Journal},

keywords = {group ring; unit group; augmentation ideal; Jacobson radical; group algebras of finite groups; group rings; groups of units; augmentation ideals; Jacobson radical},

language = {eng},

number = {1},

pages = {149-157},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {Unit groups of group algebras of some small groups},

url = {http://eudml.org/doc/262013},

volume = {64},

year = {2014},

}

TY - JOUR

AU - Tang, Gaohua

AU - Wei, Yangjiang

AU - Li, Yuanlin

TI - Unit groups of group algebras of some small groups

JO - Czechoslovak Mathematical Journal

PY - 2014

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 64

IS - 1

SP - 149

EP - 157

AB - Let $FG$ be a group algebra of a group $G$ over a field $F$ and ${\mathcal {U}}(FG)$ the unit group of $FG$. It is a classical question to determine the structure of the unit group of the group algebra of a finite group over a finite field. In this article, the structure of the unit group of the group algebra of the non-abelian group $G$ with order $21$ over any finite field of characteristic $3$ is established. We also characterize the structure of the unit group of $FA_4$ over any finite field of characteristic $3$ and the structure of the unit group of $FQ_{12}$ over any finite field of characteristic $2$, where $Q_{12}=\langle x, y; x^6=1, y^2=x^3, x^y=x^{-1} \rangle $.

LA - eng

KW - group ring; unit group; augmentation ideal; Jacobson radical; group algebras of finite groups; group rings; groups of units; augmentation ideals; Jacobson radical

UR - http://eudml.org/doc/262013

ER -

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