JOURNAL BROWSE
Search
Advanced SearchSearch Tips
A CHARACTERIZATION OF THE UNIT GROUP IN ℤ[T×C2]
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
A CHARACTERIZATION OF THE UNIT GROUP IN ℤ[T×C2]
Bilgin, Tevfik; Kusmus, Omer; Low, Richard M.;
  PDF(new window)
 Abstract
Describing the group of units of the integral group ring , for a finite group G, is a classical and open problem. In this note, we show that ){\sim_
 Keywords
integral group ring;unit problem;
 Language
English
 Cited by
 References
1.
P. J. Allen and C. Hobby, A characterization of units in $\mathbb{Z}[A_4]$, J. Algebra 66 (1980), no. 2, 534-543. crossref(new window)

2.
P. J. Allen and C. Hobby, A characterization of units in $\mathbb{Z}[S_4]$, Comm. Algebra 16 (1988), no. 7, 1479-1505. crossref(new window)

3.
T. Bilgin, Characterization of $U_1(\mathbb{Z}C_{12})$, Int. J. Pure Appl. Math. 14 (2004), no. 4, 531-535.

4.
S. Galovich, I. Reiner, and S. Ullom, Class groups for integral representations of metacyclic groups, Mathematika 19 (1972), 105-111. crossref(new window)

5.
G. Higman, Units in Group Rings, D. Phil. Thesis, University of Oxford, Oxford, 1940.

6.
G. Higman, The units of group rings, Proc. London Math. Soc. 46 (1940), 231-248.

7.
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. crossref(new window)

8.
E. Jespers, Free normal complements and the unit group of integral group rings, Proc. Amer. Math. Soc. 122 (1994), no. 1, 59-66. crossref(new window)

9.
E. Jespers, Bicyclic units in some integral group rings, Canad. Math. Bull. 38 (1995), no. 1, 80-86. crossref(new window)

10.
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.

11.
E. Jespers and M. M. Parmenter, Units of group rings of groups of order 16, Glasgow Math. J. 35 (1993), no. 3, 367-379. crossref(new window)

12.
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. crossref(new window)

13.
G. Karpilovsky, Commutative Group Algebras, Marcel Dekker, New York, 1983.

14.
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.

15.
O. Kusmus and I. H. Denizler, Construction of units in $\mathbb{Z}C_{24}$, Int. J. Algebra. 8, 471-477. - preprint.

16.
Y. Li, Units of $\mathbb{Z}(G{\times}C_2)$, Quaestiones Mathematicae 21 (1998), 201-218. crossref(new window)

17.
R. M. Low, Units in Integral Group Rings for Direct Products, Ph.D. Thesis, Western Michigan University, Kalamazoo, MI, 1998.

18.
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. crossref(new window)

19.
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.

20.
M. M. Parmenter, Free torsion-free normal complements in integral group rings, Commun. Algebra 21 (1993), no. 10, 3611-3617. crossref(new window)

21.
D. S. Passman and P. F. Smith, Units in integral group rings, J. Algebra 69 (1981), no. 1, 213-239. crossref(new window)

22.
J. Ritter and S. K. Sehgal, Integral group rings of some p-groups, Canad. J. Math. 34 (1982), no. 1, 233-246. crossref(new window)

23.
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. crossref(new window)

24.
S. K. Sehgal, Units in Integral Group Rings, Longman Scientific & Technical, Essex, 1993.