Sharma, Sneh A split embedding for groups of class three. (English) Zbl 1009.20007 Bull. Calcutta Math. Soc. 94, No. 1, 49-52 (2002). Let \(G\) be a finite group and \(G_n\) be the \(n\)-th lower central subgroup of \(G\). Denote by \(A_G\) the augmentation ideal of the integral group ring \(\mathbb{Z} G\). It is known [G. Losey, Can. J. Math. 26, 962-977 (1974; Zbl 0255.20026)] that if \(G\) is a finite group of odd order, then the canonical homomorphism \(G_3/G_4\to A^3_G/A^4_G\) is a split monomorphism. Using the cocycle machinery of I. B. S. Passi [J. Algebra 9, 152-182 (1968; Zbl 0159.31503)], in this paper the author gives a new proof of this result when \(G\) is a finite \(p\)-group of class 3 with \(p>2\). Reviewer: S.V.Mihovski (Plovdiv) MSC: 20C05 Group rings of finite groups and their modules (group-theoretic aspects) 20D15 Finite nilpotent groups, \(p\)-groups 20F14 Derived series, central series, and generalizations for groups 16S34 Group rings Keywords:finite groups; lower central subgroups; augmentation ideals; integral group rings; split monomorphisms; finite \(p\)-groups PDF BibTeX XML Cite \textit{S. Sharma}, Bull. Calcutta Math. Soc. 94, No. 1, 49--52 (2002; Zbl 1009.20007)