Group Theory for Tetramethylethylene, II

Mohammad Reza Darafsheh^1,*, Ali Moghani² and Soroor Naghdi Sedeh²

¹ School of Mathematics, College of Science, University of Tehran, 14174 Tehran, Iran
² Department of Color Physics, Institute for Colorant, Paint and Coating (ICPC), 16765 Tehran, Iran
* Corresponding author: E-mail: darafsheh@ut.ac.ir

Abstract
The maturated and unmaturated groups have been introduced by S. Fujita who used them in the markaracter table and the Q-conjugacy character table of a finite group. Fujita introduced more concise forms called the Q-conjugacy characters with integer-valued of the irreducible characters of finite groups and applied his results in this area of research to enumerate isomers of molecules. In this paper using GAP program all integer-valued characters of the full non-rigid group (f-NRG) of tetramethylethylene (2,3-dimethylbut-2-ene) is calculated by the Q-conjugacy relationships. It is shown that this group has 29 dominant classes (similarly, Q-conjugacy characters) such that 16 of them are unmaturated (similarly, Q-conjugacy characters such that they are the sum of two irreducible characters). Then the markaracter table and Q-conjugacy character table of the f-NRG of tetramethylethylene are derived for the first time.

Keywords: Full non-rigid group, markaracter table, Q-conjugacy character table, tetramethylethylene (2,3-dimethylbut-2-ene).