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Group rings and the norm groups. (English) Zbl 0807.11048
The author’s purpose is to determine the set of all polynomials in \(\mathbb{Z}[t]\) with \(f(t)\) dividing \(t^ n-1\) of a form called \(H\)-type (which means that if \(G\) is a cyclic group of order \(a\) generated by \(\sigma\) then \(a^{f(\sigma)}=1\) implies the existence of a \(b\) with \(a=b^{(\sigma^ n -1)/ f(\sigma)}\)).
Reviewer: R.Mollin (Calgary)
MSC:
11R09 Polynomials (irreducibility, etc.)
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References:
[1] S. Endo and T. Miyata: Quasi-permutation modules over finite groups. J. Math. Soc. Japan, 25, 397-421 (1973). · Zbl 0253.20012
[2] W. Hurlimann: A cyclotomic Hilbert 90 theorem. Arch. Math., 43, 25-26 (1984). · Zbl 0522.12021
[3] S. lyanaga (ed.): The Theory of Numbers. North Holland, American Elsevier, New York (1975). · Zbl 0327.12001
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