Q-Conjugacy character table for the non-rigid group of 2,3-dimethylbutane

• Main Authors: MOHAMMAD REZA DARAFSHEH, ALI MOGHANI
• Format: Article
• Language: English
• Published: Serbian Chemical Society 2009-01-01
• Series: Journal of the Serbian Chemical Society
• Subjects: full non-rigid group; Q-conjugacy character; 2; 3-dimethylbutane
• Online Access: http://www.shd.org.rs/JSCS/Vol74/No1/05_4096_3807.pdf

Maturated and unmaturated groups were introduced by the Japanese chemist Shinsaku Fujita, who used them in the markaracter table and the Q-conjugacy character table of a finite group. He then applied his results in this area of research to enumerate isomers of molecules. Using the non-rigid group theory, it was shown by the second author that the full non-rigid (f-NRG) group of 2,3--dimethylbutane is isomorphic to the group (Z3×Z3×Z3×Z3):Z2 of order 162 with 54 conjugacy classes. Here (Z3×Z3×Z3×Z3):Z2 denotes the semi direct product of four copies of Z3 by Z2, where Zn is a cyclic group of order n. In this paper, it is shown with the GAP program that this group has 30 dominant classes (similarly, Q-conjugacy characters) and that 24 of them are unmatured (similarly, Q-conjugacy characters such that they are the sum of two irreducible characters). Then, the Q-conjugacy character table of the unmatured full non-rigid group 2,3-dimethylbutane is derived.