ON THE STRUCTURE OF THE UNITARY SUBGROUP OF THE GROUP ALGEBRA 𝔽_2^qD_2ⁿ

Abstract

We discuss the structure of the unitary subgroup V * (F 2 q D 2 n ) of the group algebra F 2 q D 2 n , where D 2 n = x, y | x 2 n−1 = y 2 = 1, xy = yx 2 n−1 −1 is the dihedral group of order 2 n and F 2 q is any finite field of characteristic 2, with 2 q elements. We will prove that V * (F 2 q D 2 n ) ∼ = C (3·2 n−2 −1)q 2 C q 2 , see Theorem 3.1.

THE GROUP OF UNITS OF GROUP ALGEBRAS OF GROUPS $D_{30}$ AND $C_3 \times D_{10}$ OVER A FINITE FIELD OF CHARACTERISTIC $3$

“…Unitary units of some modular group algebras have been studied in [2,3]. In [16,17], the structure of the unitary subgroup of the group algebra F D 2 n and F (QD 16 ), where QD 16 is the quasi-dihedral group of order 16 and p = 2, has been obtained.…”

On the unitary units of the group algebra 𝔽2kQ16

“…In [17,18], Raza and Ahmad determined the structure of unitary unit group of the group algebra F 2 m M 16 and F 2 q D 2 n . For detailed background, we refer a comprehensive survey of Bovdi [1].…”