×

Wreath products in the unit group of modular group algebras of 2-groups of maximal class. (English) Zbl 1004.16027

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.

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

Citations:

Zbl 0702.16021
PDFBibTeX XMLCite
Full Text: arXiv EuDML