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Double Actions of Groups
Abstract
In this work, we present the
concept of double action of a group on a set as a new concept in literature, which opens up
the way for applying rich amount of algebraic topological facts and methods in
the algebraic topology. Besides of this, we give some expository examples of
this new concept. We also express the definition of a double action via
permutations as similar to the definition of an action on a set of groups via
permutations. We investigate some characterizations about the double actions.
Also we prove an adaptation of Cayley’s theorem in the case of the double action.
Keywords
References
- 1- Alp, M., Pullback Crossed Modules of Algebroids, Iran. J. Sci. Technol. Trans. A Sci., No.A1, 32, (2008), 1-5
- 2- Brown, R., Topology and Groupoids, BookSurge LLC, Deganwy, United Kingdom, 2006
- 3- Derek, J.S.R., A Course in the Theory of Groups, Springer-Verlag, New York, USA, 1996
- 4- Gursoy, M.H., Actions of Vector Groupoids, Bull. Iranian Math. Soc., 40, No.3, (2014), 565-582
- 5- Norrie, K., Actions and Automorphisms of Crossed Modules, Bull. Soc. Math. France, 118, (1990), 129-146
Details
Primary Language
English
Subjects
-
Journal Section
Research Article
Authors
Publication Date
September 30, 2019
Submission Date
December 1, 2018
Acceptance Date
August 19, 2019
Published in Issue
Year 2019 Volume: 40 Number: 3
APA
Gürsoy, M. H. (2019). Double Actions of Groups. Cumhuriyet Science Journal, 40(3), 612-623. https://doi.org/10.17776/csj.491048
AMA
1.Gürsoy MH. Double Actions of Groups. CSJ. 2019;40(3):612-623. doi:10.17776/csj.491048
Chicago
Gürsoy, Mustafa Habil. 2019. “Double Actions of Groups”. Cumhuriyet Science Journal 40 (3): 612-23. https://doi.org/10.17776/csj.491048.
EndNote
Gürsoy MH (September 1, 2019) Double Actions of Groups. Cumhuriyet Science Journal 40 3 612–623.
IEEE
[1]M. H. Gürsoy, “Double Actions of Groups”, CSJ, vol. 40, no. 3, pp. 612–623, Sept. 2019, doi: 10.17776/csj.491048.
ISNAD
Gürsoy, Mustafa Habil. “Double Actions of Groups”. Cumhuriyet Science Journal 40/3 (September 1, 2019): 612-623. https://doi.org/10.17776/csj.491048.
JAMA
1.Gürsoy MH. Double Actions of Groups. CSJ. 2019;40:612–623.
MLA
Gürsoy, Mustafa Habil. “Double Actions of Groups”. Cumhuriyet Science Journal, vol. 40, no. 3, Sept. 2019, pp. 612-23, doi:10.17776/csj.491048.
Vancouver
1.Mustafa Habil Gürsoy. Double Actions of Groups. CSJ. 2019 Sep. 1;40(3):612-23. doi:10.17776/csj.491048