Konovalov, Alexander B. Wreath products in the unit group of modular group algebras of 2-groups of maximal class. (English) Zbl 1004.16027 Acta Math. Acad. Paedagog. Nyházi. (N.S.) 17, 141-149 (2001). Let \(KG\) be a modular group algebra of the \(2\)-group \(G\) of maximal class. The author proves that the normalized unit group \(U(KG)\) posesses a section which is isomorphic to the wreath product of a group of order two with the commutator subgroup of the group \(G\). This is the answer to a question of A. Shalev [Suppl. Rend. Circ. Mat. Palermo, II. Ser. 23, 279-288 (1990; Zbl 0702.16021)] in the special case of a \(2\)-group of maximal class. Reviewer: A.A.Bovdi (Debrecen) MSC: 16U60 Units, groups of units (associative rings and algebras) 20C05 Group rings of finite groups and their modules (group-theoretic aspects) 16S34 Group rings 20D15 Finite nilpotent groups, \(p\)-groups Keywords:modular group algebras; unit groups; nilpotency class; wreath products; 2-groups of maximal class Citations:Zbl 0702.16021 PDFBibTeX XMLCite \textit{A. B. Konovalov}, Acta Math. Acad. Paedagog. Nyházi. (N.S.) 17, 141--149 (2001; Zbl 1004.16027) Full Text: arXiv EuDML