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
)