| Title:
|
Crossed product of cyclic groups (English) |
| Author:
|
Agore, Ana-Loredana |
| Author:
|
Frățilă, Dragoş |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
60 |
| Issue:
|
4 |
| Year:
|
2010 |
| Pages:
|
889-901 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| 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. (English) |
| Keyword:
|
cyclic groups |
| Keyword:
|
crossed product of groups |
| Keyword:
|
Chinese Remainder Theorem |
| MSC:
|
20B05 |
| MSC:
|
20B35 |
| MSC:
|
20D06 |
| MSC:
|
20D40 |
| MSC:
|
20E22 |
| idZBL:
|
Zbl 1208.20030 |
| idMR:
|
MR2738954 |
| . |
| Date available:
|
2010-11-20T13:51:18Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140791 |
| . |
| Reference:
|
[1] Adem, A., Milgram, R. J.: Cohomology of Finite Groups, 2nd Edition.Springer Berlin (2004). MR 2035696 |
| Reference:
|
[2] Agore, A. L.: Constructions in group theory.Dissertation University of Bucharest Bucharest (2008). |
| Reference:
|
[3] Agore, A. L., Militaru, G.: Crossed product of groups applications.Arabian J. Sci. Eng. 33 (2008), 1-17. Zbl 1186.20021, MR 2500024 |
| Reference:
|
[4] Bechtell, H.: The Theory of Groups.Addison-Wesley Publishing Company Reading (1971). Zbl 0229.20001, MR 0284490 |
| Reference:
|
[5] Grillet, P. A.: Abstract Algebra, 2nd Edition. Graduate Texts in Mathematics 242.Springer New York (2007). MR 2330890 |
| Reference:
|
[6] Hölder, O.: Bildung zusammengesetzter Gruppen.Math. Ann. 46 (1895), 321-422. MR 1510888, 10.1007/BF01450217 |
| Reference:
|
[7] Rotman, J.: An introduction to the theory of groups, 4th Edition. Graduate Texts in Mathematics 148.Springer New York (1995). MR 1307623 |
| Reference:
|
[8] Weibel, C.: An Introduction to Homological Algebra.Cambridge Univ. Press Cambridge (1994). Zbl 0797.18001, MR 1269324 |
| . |
