A note on the unit group of
Authors:
P. J. Allen and C. Hobby
Journal:
Proc. Amer. Math. Soc. 99 (1987), 914
MSC:
Primary 20C05; Secondary 16A26, 20C10
MathSciNet review:
866420
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Abstract 
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Abstract: The group of units of augmentation 1 in is characterized as the group of all doubly stochastic matrices in . Two normal complements are presented, one of which is torsion free while the other contains elements of order 2.
 [1]
P.
J. Allen and C.
Hobby, A characterization of units in
𝑍[𝐴₄], J. Algebra 66 (1980),
no. 2, 534–543. MR 593609
(81k:20012), http://dx.doi.org/10.1016/00218693(80)901027
 [2]
G.
H. Cliff, S.
K. Sehgal, and A.
R. Weiss, Units of integral group rings of metabelian groups,
J. Algebra 73 (1981), no. 1, 167–185. MR 641639
(83i:20006), http://dx.doi.org/10.1016/00218693(81)903537
 [3]
I.
Hughes and K.
R. Pearson, The group of units of the integral group ring
𝑍𝑆₃, Canad. Math. Bull. 15
(1972), 529–534. MR 0325743
(48 #4089)
 [4]
C. Milies, The units of the integral group ring , Bol. Soc. Brasil. Mat. 4 (1972), 8592.
 [5]
Morris
Newman, Integral matrices, Academic Press, New York, 1972.
Pure and Applied Mathematics, Vol. 45. MR 0340283
(49 #5038)
 [6]
D.
S. Passman and P.
F. Smith, Units in integral group rings, J. Algebra
69 (1981), no. 1, 213–239. MR 613869
(82h:20009), http://dx.doi.org/10.1016/00218693(81)901393
 [7]
Olga
Taussky, Matrices of rational
integers, Bull. Amer. Math. Soc. 66 (1960), 327–345. MR 0120237
(22 #10994), http://dx.doi.org/10.1090/S000299041960104399
 [1]
 P. J. Allen and C. Hobby, A characterization of units in , J. Algebra 66 (1980), 534543. MR 593609 (81k:20012)
 [2]
 G. H. Cliff, S. K. Sehgal, and A. R. Weiss, Units of integral group rings of metabelian groups, J. Algebra 73 (1981), 167185. MR 641639 (83i:20006)
 [3]
 I. Hughes and K. R. Pearson, The group of units of the integral group ring , Canad. Math. Bull. 15 (1972), 529534. MR 0325743 (48:4089)
 [4]
 C. Milies, The units of the integral group ring , Bol. Soc. Brasil. Mat. 4 (1972), 8592.
 [5]
 M. Newman, Integral matrices, Academic Press, New York, 1972. MR 0340283 (49:5038)
 [6]
 D. S. Passman and P. F. Smith, Units in integral group rings, J. Algebra 69 (1981), 213239. MR 613869 (82h:20009)
 [7]
 O. Taussky, Matrices of rational integers, Bull. Amer. Math. Soc. 66 (1960), 327345. MR 0120237 (22:10994)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0002993919870866420X
PII:
S 00029939(1987)0866420X
Article copyright:
© Copyright 1987 American Mathematical Society
