Crossed product of cyclic groups

Ana-Loredana Agore; Dragoş Frățilă

Czechoslovak Mathematical Journal (2010)

  • Volume: 60, Issue: 4, page 889-901
  • ISSN: 0011-4642

Abstract

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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.

How to cite

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Agore, Ana-Loredana, and Frățilă, Dragoş. "Crossed product of cyclic groups." Czechoslovak Mathematical Journal 60.4 (2010): 889-901. <http://eudml.org/doc/196958>.

@article{Agore2010,
abstract = {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.},
author = {Agore, Ana-Loredana, Frățilă, Dragoş},
journal = {Czechoslovak Mathematical Journal},
keywords = {cyclic groups; crossed product of groups; Chinese Remainder Theorem; cyclic groups; crossed products of groups; generators and relations; extensions of groups},
language = {eng},
number = {4},
pages = {889-901},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Crossed product of cyclic groups},
url = {http://eudml.org/doc/196958},
volume = {60},
year = {2010},
}

TY - JOUR
AU - Agore, Ana-Loredana
AU - Frățilă, Dragoş
TI - Crossed product of cyclic groups
JO - Czechoslovak Mathematical Journal
PY - 2010
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 60
IS - 4
SP - 889
EP - 901
AB - 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.
LA - eng
KW - cyclic groups; crossed product of groups; Chinese Remainder Theorem; cyclic groups; crossed products of groups; generators and relations; extensions of groups
UR - http://eudml.org/doc/196958
ER -

References

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  1. Adem, A., Milgram, R. J., Cohomology of Finite Groups, 2nd Edition, Springer Berlin (2004). (2004) MR2035696
  2. Agore, A. L., Constructions in group theory, Dissertation University of Bucharest Bucharest (2008). (2008) 
  3. Agore, A. L., Militaru, G., Crossed product of groups applications, Arabian J. Sci. Eng. 33 (2008), 1-17. (2008) Zbl1186.20021MR2500024
  4. Bechtell, H., The Theory of Groups, Addison-Wesley Publishing Company Reading (1971). (1971) Zbl0229.20001MR0284490
  5. Grillet, P. A., Abstract Algebra, 2nd Edition. Graduate Texts in Mathematics 242, Springer New York (2007). (2007) MR2330890
  6. Hölder, O., 10.1007/BF01450217, Math. Ann. 46 (1895), 321-422. (1895) MR1510888DOI10.1007/BF01450217
  7. Rotman, J., An introduction to the theory of groups, 4th Edition. Graduate Texts in Mathematics 148, Springer New York (1995). (1995) MR1307623
  8. Weibel, C., An Introduction to Homological Algebra, Cambridge Univ. Press Cambridge (1994). (1994) Zbl0797.18001MR1269324

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