Previous |  Up |  Next


cyclic groups; crossed product of groups; Chinese Remainder Theorem
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.
[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
[4] Bechtell, H.: The Theory of Groups. Addison-Wesley Publishing Company Reading (1971). MR 0284490 | Zbl 0229.20001
[5] Grillet, P. A.: Abstract Algebra, 2nd Edition. Graduate Texts in Mathematics 242. Springer New York (2007). MR 2330890
[6] Hölder, O.: Bildung zusammengesetzter Gruppen. Math. Ann. 46 (1895), 321-422. DOI 10.1007/BF01450217 | MR 1510888
[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
Partner of
EuDML logo