Geodesic
Integral Group Rings of Some p-Groups
Canadian journal of mathematics, Tome 34 (1982) no. 1, pp. 233-246

Voir la notice de l'article provenant de la source Cambridge University Press

1. Introduction. The group of units, , of the integral group ring of a finite non-abelian group G is difficult to determine. For the symmetric group of order 6 and the dihedral group of order 8 this was done by Hughes-Pearson [3] and Polcino Milies [5] respectively. Allen and Hobby [1] have computed , where A4 is the alternating group on 4 letters. Recently, Passman-Smith [6] gave a nice characterization of where D 2p is the dihedral group of order 2p and p is an odd prime. In an earlier paper [2] Galovich-Reiner-Ullom computed when G is a metacyclic group of order pq with p a prime and q a divisor of (p – 1). In this note, using the fibre product decomposition as in [2], we give a description of the units of the integral group rings of the two noncommutative groups of order p 3, p an odd prime. In fact, for these groups we describe the components of Z G in the Wedderburn decomposition of Q G. 
Ritter, Jürgen; Sehgal, Sudarshan. Integral Group Rings of Some p-Groups. Canadian journal of mathematics, Tome 34 (1982) no. 1, pp. 233-246. doi: 10.4153/CJM-1982-016-5
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[5] 5. Polcino Milies, C., The units of the integral group ring ZZ)4, Bol. Soc. Brasil. Mat. 4 (1972), 85–92. Google Scholar

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[7] 7. Sehgal, S. K., Topics in group rings (Dekker, New York, 1978). Google Scholar

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