Units of group algebras of non-Abelian groups of order 16 and exponent 4 over \(\mathbb F_{2^k}\).
Let \(G=\langle x,y\mid x^4=1,\;y^4=1,\;(xy)^2=1,\;xy^3=x^3y\rangle\) (\(G=\langle x,y\mid x^4=1,\;y^4=1,\;(xy)^2=1,\;y^3xy=x^3\rangle\)), groups of order 16, \(F_{2^k}G\) the group algebra over the Galois-field and \(V\) its group of normalized units. Continuing the research of several papers such as the author's [Int. J. Algebra Comput. 20, No. 5, 721-729 (2010; Zbl 1205.16031)], the paper by \textit{L. Creedon} and \textit{J. Gildea} [Can. Math. Bull. 54, No. 2, 237-243 (2011; Zbl 1242.16033)], the author determines the structure of the group \(V\) as follows: \((C_2^{10k}\rtimes C_4^k)\rtimes(C_2^k\times C_4^k)\) (\(((C_2^{8k}\rtimes C_4^k)\rtimes C_4^k)\rtimes(C_2^k\times C_4^k)\)).
scientific article; zbMATH DE number 6124389