References
-
P. J. Allen and C. Hobby, A characterization of units in
$\mathbb{Z}[A_4]$ , J. Algebra 66 (1980), no. 2, 534-543. https://doi.org/10.1016/0021-8693(80)90102-7 -
P. J. Allen and C. Hobby, A characterization of units in
$\mathbb{Z}[S_4]$ , Comm. Algebra 16 (1988), no. 7, 1479-1505. https://doi.org/10.1080/00927878808823639 -
T. Bilgin, Characterization of
$U_1(\mathbb{Z}C_{12})$ , Int. J. Pure Appl. Math. 14 (2004), no. 4, 531-535. - S. Galovich, I. Reiner, and S. Ullom, Class groups for integral representations of metacyclic groups, Mathematika 19 (1972), 105-111. https://doi.org/10.1112/S0025579300005015
- G. Higman, Units in Group Rings, D. Phil. Thesis, University of Oxford, Oxford, 1940.
- G. Higman, The units of group rings, Proc. London Math. Soc. 46 (1940), 231-248.
-
I. Hughes and K. R. Pearson, The group of units of the integral group ring
$\mathbb{Z}S_3$ , Canad. Math. Bull. 15 (1972), 529-534. https://doi.org/10.4153/CMB-1972-093-1 - E. Jespers, Free normal complements and the unit group of integral group rings, Proc. Amer. Math. Soc. 122 (1994), no. 1, 59-66. https://doi.org/10.1090/S0002-9939-1994-1221725-1
- E. Jespers, Bicyclic units in some integral group rings, Canad. Math. Bull. 38 (1995), no. 1, 80-86. https://doi.org/10.4153/CMB-1995-010-4
-
E. Jespers and M. M. Parmenter, Bicyclic units in
$\mathbb{Z}S_3$ , Bull. Soc. Math. Belg. Ser. B 44 (1992), no. 2, 141-146. - E. Jespers and M. M. Parmenter, Units of group rings of groups of order 16, Glasgow Math. J. 35 (1993), no. 3, 367-379. https://doi.org/10.1017/S0017089500009952
- E. Jespers, A. Pita, A. del Rio, M. Ruiz, and P. Zalesskii, Groups of units of integral group rings commensurable with direct products of free-by-free groups, Adv. Math. 212 (2007), no. 2, 692-722. https://doi.org/10.1016/j.aim.2006.11.005
- G. Karpilovsky, Commutative Group Algebras, Marcel Dekker, New York, 1983.
-
I. G. Kelebek and T. Bilgin, Characterization of
$U_1(\mathbb{Z}[C_n\;\times\;K_4])$ , Eur. J. Pure Appl. Math. 7 (2014), no. 4, 462-471. -
O. Kusmus and I. H. Denizler, Construction of units in
$\mathbb{Z}C_{24}$ , Int. J. Algebra. 8, 471-477. - preprint. -
Y. Li, Units of
$\mathbb{Z}(G{\times}C_2)$ , Quaestiones Mathematicae 21 (1998), 201-218. https://doi.org/10.1080/16073606.1998.9632041 - R. M. Low, Units in Integral Group Rings for Direct Products, Ph.D. Thesis, Western Michigan University, Kalamazoo, MI, 1998.
-
R. M. Low, On the units of the integral group ring
$\mathbb{Z}[G{\times}C_p]$ , J. Algebra Appl. 7 (2008), no. 3, 393-403. https://doi.org/10.1142/S0219498808002898 - M. M. Parmenter, Torsion-free normal complements in unit groups of integral group rings, C. R. Math. Rep. Acad. Sci. Canada 12 (1990), no. 4, 113-118.
- M. M. Parmenter, Free torsion-free normal complements in integral group rings, Commun. Algebra 21 (1993), no. 10, 3611-3617. https://doi.org/10.1080/00927879308824751
- D. S. Passman and P. F. Smith, Units in integral group rings, J. Algebra 69 (1981), no. 1, 213-239. https://doi.org/10.1016/0021-8693(81)90139-3
- J. Ritter and S. K. Sehgal, Integral group rings of some p-groups, Canad. J. Math. 34 (1982), no. 1, 233-246. https://doi.org/10.4153/CJM-1982-016-5
- J. Ritter and S. K. Sehgal, Units of group rings of solvable and Frobenius groups over large rings of cyclotomic integers, J. Algebra 158 (1993), no. 1, 116-129. https://doi.org/10.1006/jabr.1993.1126
- S. K. Sehgal, Units in Integral Group Rings, Longman Scientific & Technical, Essex, 1993.