Related papers: Units in $FD_{2p^m}$

In this paper, we present the structure of the group of *-unitary units in the group algebra $FD_{2p}$, where $F$ is a finite field of characteristic $p > 2$, $D_{2p}$ is the dihedral group of order $2p$, and * is the canonical involution…

Let $p$ be an odd prime, $D_{2p}$ be the dihedral group of order 2p, and $F_{2}$ be the finite field with two elements. If * denotes the canonical involution of the group algebra $F_2D_{2p}$, then bicyclic units are unitary units. In this…

Let $p$ be a prime and $F$ be a finite field of characteristic $p$. Suppose that $FG$ is the group algebra of the finite $p$-group $G$ over the field $F$. Let $V(FG)$ denote the group of normalized units in $FG$ and let $V_*(FG)$ denote the…

Let $FG$ be the group algebra of a finite $p$-group $G$ over a finite field $F$ of positive characteristic $p$. Let $\cd$ be an involution of the algebra $FG$ which is a linear extension of an anti-automorphism of the group $G$ to $FG$. If…

Let $F_{q}$ be any finite field of characteristic $p>0$ having $q = p^{n}$ elements. In this paper, we have obtained the complete structure of unit groups of group algebras $F_{q}[QD_{2^k}]$, for $k = 4$ and $5$, for any prime $p>0$, where…

Let p be an odd prime, F the field of p elements and G a finite abelian p-group with an arbitrary involutory automorphism. Extend this automorphism to the group algebra FG and consider the unitary and the symmetric normalized units of FG.…

Let $FG$ be the group algebra of a finite $p$-group $G$ over a finite field $F$ of characteristic $p$ and $*$ the classical involution of $FG$. The $*$-unitary subgroup of $FG$, denoted by $V_*(FG)$, is defined to be the set of all…

Let $D_{n}$ be the dihedral group of order $n$. The structure of the unit group $U(F(C_3 \times D_{10}))$ of the group algebra $F(C_3 \times D_{10})$ over a finite field $F$ of characteristic $3$ is given in \cite{sh13}. In this article,…

Let $FG$ be the group algebra of a finite $2$-group $G$ over a finite field $F$ of characteristic two and $\circledast$ an involution which arises from $G$. The $\circledast$-unitary subgroup of $FG$, denoted by $V_{\circledast}(FG)$, is…

Let KG be a group algebra of a finite p-group G over a finite field K of characteristic p. We compute the order of the unitary subgroup of the group of units when G is either an extraspecial 2-group or the central product of such a group…

Let F be the field of two elements and G a finite abelian 2-group with an involutory automorphism. The extension of this automorphism to the group algebra FG is called an involutory involution. This determines the groups of unitary and…

Let $p$ be a prime and $\mathbb{F}_p$ be a finite field of $p$ elements. Let $\mathbb{F}_pG$ denote the group algebra of the finite $p$-group $G$ over the field $\mathbb{F}_p$ and $V(\mathbb{F}_pG)$ denote the group of normalized units in…

The structure of the unitary unit group of the group algebra ${\F}_{2^k} Q_{8}$ is described as a Hamiltonian group.

Let $F$ be a finite field of characteristic $p>0$ with $q = p^{n}$ elements. In this paper, a complete characterization of the unit groups $U(FG)$ of group algebras $FG$ for the abelian groups of order $32$, over finite field of…

Let $C_n$, $Q_n$ and $D_n$ be the cyclic group, the quaternion group and the dihedral group of order $n$, respectively. The structures of the unit groups of the finite group algebras $FQ_{12}$ and $F(C_2 \times Q_{12})$ over a finite field…

We consider finite dimensional representations of the dihedral group $D_{2p}$ over an algebraically closed field of characteristic two where $p$ is an odd integer and study the degrees of generating and separating polynomials in the…

In this paper, we construct an infinite families of group $G$ of order $4p^m$ which can be an automorphism group of some regular polytope with type $\{p, 2p\}$, where $m \geq 3$ and $p$ is an odd prime. For $p=3$, our polytopes are the…

Let $F$ be a finite field of characteristic $p$. The structures of the unit groups of group algebras over $F$ of the three groups $D_{24}$, $S_4$ and $SL(2, \mathbb{Z}_3)$ of order $24$ are completely described in \cite{K4, SM, SM1, FM,…

Let $G$ be a finite group and $H$ a normal subgroup of prime index $p$. Let $V$ be an irreducible ${\mathbb F}H$-module and $U$ a quotient of the induced ${\mathbb F}G$-module $V\kern-3pt\uparrow$. We describe the structure of $U$, which is…

In this paper we study embeddings of unitriangular groups UT$_n(\mathbb{F}_p)$ arising under adjunction of roots. We construct embeddings of UT$_n(\mathbb{F}_p)$ in UT$_m(\mathbb{F}_p)$, for $n \geq 2$, $m=(n-1)p^s + 1$, $s \in…