Units in $\mathbb{Z}_2(C_2\times D_\infty)$

Document Type: Research Paper


1 Indian Institute of Technology Delhi

2 Kamla Nehru College, University of Delhi, Delhi

3 Department of Mathematics, University of Delhi, Delhi


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.


Main Subjects

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.