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Sharma, R, Yadav, Pooja, Joshi, Kanchan. (1391). Units in z2(c2 x d∞). , 1(4), 33-41. doi: 10.22108/ijgt.2012.1589
R Sharma; Pooja Yadav; Kanchan Joshi. "Units in z2(c2 x d∞)". , 1, 4, 1391, 33-41. doi: 10.22108/ijgt.2012.1589
Sharma, R, Yadav, Pooja, Joshi, Kanchan. (1391). 'Units in z2(c2 x d∞)', , 1(4), pp. 33-41. doi: 10.22108/ijgt.2012.1589
Sharma, R, Yadav, Pooja, Joshi, Kanchan. Units in z2(c2 x d∞). , 1391; 1(4): 33-41. doi: 10.22108/ijgt.2012.1589

Units in z2(c2 x d∞)

International Journal of Group Theory
مقاله 4، دوره 1، شماره 4، اسفند 2012، صفحه 33-41    اصل مقاله (415.01 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22108/ijgt.2012.1589
نویسندگان
R Sharma* 1؛ Pooja Yadav2؛ Kanchan Joshi3
1Indian Institute of Technology Delhi
2Kamla Nehru College, University of Delhi, Delhi
3Department of Mathematics, University of Delhi, Delhi
چکیده
In this paper we consider the group algebra $R(C_2\times‎ ‎D_\infty)$‎. ‎It is shown that $R(C_2\times D_\infty)$ can be‎ ‎represented by a $4\times 4$ block circulant matrix‎. ‎It is also‎ ‎shown that $\mathcal{U}(\mathbb{Z}_2(C_2\times D_\infty))$ is‎ ‎infinitely generated‎.
کلیدواژه‌ها
Unit Group؛ infinite dihedral group؛ Circulant Matrices
مراجع
V. A. Artamonov and A. A. Bovdi (1991) Integral group rings: groups of invertible elements and classical $K$-theory J. Soviet Math. 57 (2), 2931-2958
A. Bovdi (1998) The group of units of a group algebras of characteristic p Publ. Math. Debrecen 52, 193-244
A. Karrass, D. Solitar and W. Magnus (1975) Combinatorial Group Theory Dover Publications, INC
J. Gildea (2011) Units of the group algebra $F_{2^k} (C_2 \times D_8)$ J. Algebra Appl. 10 (4), 643-647
J. Gildea (2011) The structure of the unitary units of the group algebra $F_{2^k}D_8$ Int. Electron. J. Algebra 9, 171-176
T. Hurley (2006) Group rings and rings of matrices Int. J. Pure Appl. Math. 31 (3), 319-335
M. Mirowicz (1991) Units in group rings of the infinite dihedral group Canad. Math. Bull. 34 (1), 83-89
D. S. Passman (1997) The Algebraic Structure of Group Rings Wiley interscience
S. K. Sehgal (1993) Units in Integral Group Rings Longman Scientific and Technical, Harlow
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