Research ArticleOpen AccessGoogle Scholar indexed
Computing the Full Non-Rigid Group of Trimethylborane and Cyclohaxane Using Wreath Product
Department of Mathematics, Federal University Gashua, Gashua, Nigeria
Department of Mathematics, University of Jos, Jos, Nigeria
- 1 Department of Mathematics, Federal University Gashua, Gashua, Nigeria
- 2 Department of Mathematics, University of Jos, Jos, Nigeria
American Journal of Computational Mathematics·Volume 10 (2020)·Pages 23–30·Published 7 January 2020·DOI10.4236/ajcm.2020.101002
Copy link · social · email
Abstract
This paper computes the group and character table of Trimethylborane and Cyclohaxane. Results show that the groups are isomorphic to the wreath products C 3 wrC 2 and C 2 wrC 6 with orders 81 and 384 and with 17 and 28 conjugacy classes respectively, where C n denotes a cyclic group of order n .
KeywordsNon-Rigid Molecule GroupTrimethylboraneCyclohaxaneWreath ProductCharacter TableConjugacy Classes
- Balasubramanian, K. (1984) Recent Applications of Group Theoretical Generators to Chemical Physics. Croatica Chemica Acta, 57, 1525-1552.
- Hamadanian, M. and Ashrafi, A.R. (2003) The Full Non-Rigid Group Theory for Trimethylamine. IJMMS, 42, 2701-2706. https://doi.org/10.1155/S0161171203205159
- Darafsher, M.R., Ashrafi, A.R. and Darasher, A. (2005) Group Theory for Tetramethylethylene. Acta Chimica Slovenica, 52, 282-287.
- Darafsher, M.R., Farjami, Y. and Ashrafi, A.R. (2005) Computing the Full Non-Rigid Group of Tetranitrocubane and Octanitrocubunae Using Wreath Product. Communications in Mathmatical and in Computer Chemistry, 54, 53-74.
- Darafsher, M.R., Ashrafi, A.R. and Darafsher, A. (2007) Non-Rigid Group Theory for 2,3-Dimethybutane. MATCH Communications in Mathematical and in Computer Chemistry, 58, 47-56.
- Moghani, A., Sedeh, S.N. and Sorouhesh, M.R. (2010) The Fujita Combinatorial Enumeration for the Non-Rigid Group of 2,4-Dimethylbenzene. Journal of the Serbian Chemical Society, 75, 91-99. https://doi.org/10.2298/JSC1001091M
- Moghadam, M.E., Karimi, T. and Algar, S. (2012) Group Theory for Non-Rigid Methyl Borane Derivatives. 22nd Iranian Algebra Seminar, Hakim Sabzevari University, Iran, 314-317.
- Moghadam, M.E., Karimi, T. and Farrokhi, M.D. (2012) Full Non-Rigid Group Theory and Symmetry of Some Diborane Deriva-tives. International Journal of Physical Sciences, 7, 73-80. https://doi.org/10.5897/IJPS11.1646
- Dixon, J.D. and Mortimer, B. (1996) Permutation Groups. Springer-Verlag, Berlin, New York. https://doi.org/10.1007/978-1-4612-0731-3
- The GAP Group (2018) GAP-Reference Manual, Release 4.8.10. 23 June 2019. https://www.gap-system.org