Article
Keywords:
cyclic groups; crossed product of groups; Chinese Remainder Theorem
Summary:
All crossed products of two cyclic groups are explicitly described using generators and relations. A necessary and sufficient condition for an extension of a group by a group to be a cyclic group is given.
References:
[1] Adem, A., Milgram, R. J.:
Cohomology of Finite Groups, 2nd Edition. Springer Berlin (2004).
MR 2035696
[2] Agore, A. L.: Constructions in group theory. Dissertation University of Bucharest Bucharest (2008).
[3] Agore, A. L., Militaru, G.:
Crossed product of groups applications. Arabian J. Sci. Eng. 33 (2008), 1-17.
MR 2500024 |
Zbl 1186.20021
[5] Grillet, P. A.:
Abstract Algebra, 2nd Edition. Graduate Texts in Mathematics 242. Springer New York (2007).
MR 2330890
[7] Rotman, J.:
An introduction to the theory of groups, 4th Edition. Graduate Texts in Mathematics 148. Springer New York (1995).
MR 1307623
[8] Weibel, C.:
An Introduction to Homological Algebra. Cambridge Univ. Press Cambridge (1994).
MR 1269324 |
Zbl 0797.18001