Geodesic
Units in Integral Group Rings of Some Metacyclic Groups
Canadian mathematical bulletin, Tome 30 (1987) no. 2, pp. 231-240

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Let p be odd prime and suppose that G = 〈a, b〉 where ap-1 = bp = 1, a-1 ba = br, and r is a generator of the multiplicative group of integers mod p. An explicit characterization of the group of normalized units V of the group ring ZG is given in terms of a subgroup of GL(p - 1, Z). This characterization is used to exhibit a normal complement for G in V.
DOI : 10.4153/CMB-1987-033-5
Mots-clés : Primary 20D15, Secondary 16A26, 20C05 
Allen, P. J.; Hobby, C. Units in Integral Group Rings of Some Metacyclic Groups. Canadian mathematical bulletin, Tome 30 (1987) no. 2, pp. 231-240. doi: 10.4153/CMB-1987-033-5
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     author = {Allen, P. J. and Hobby, C.},
     title = {Units in {Integral} {Group} {Rings} of {Some} {Metacyclic} {Groups}},
     journal = {Canadian mathematical bulletin},
     pages = {231--240},
     year = {1987},
     volume = {30},
     number = {2},
     doi = {10.4153/CMB-1987-033-5},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1987-033-5/}
}
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