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.
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.
Sharma, R., Yadav, P., Joshi, K. (2012). Units in $\mathbb{Z}_2(C_2\times D_\infty)$. International Journal of Group Theory, 1(4), 33-41. doi: 10.22108/ijgt.2012.1589
MLA
R Sharma; Pooja Yadav; Kanchan Joshi. "Units in $\mathbb{Z}_2(C_2\times D_\infty)$". International Journal of Group Theory, 1, 4, 2012, 33-41. doi: 10.22108/ijgt.2012.1589
HARVARD
Sharma, R., Yadav, P., Joshi, K. (2012). 'Units in $\mathbb{Z}_2(C_2\times D_\infty)$', International Journal of Group Theory, 1(4), pp. 33-41. doi: 10.22108/ijgt.2012.1589
VANCOUVER
Sharma, R., Yadav, P., Joshi, K. Units in $\mathbb{Z}_2(C_2\times D_\infty)$. International Journal of Group Theory, 2012; 1(4): 33-41. doi: 10.22108/ijgt.2012.1589