Algebra Commons^™

Study On The Q-Conjugacy Relations For The Janko Groups, Ali Moghani

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we consider all the Janko sporadic groups J₁, J₂, J₃ and J₄ (with orders 175560, 604800, 50232960 and 86775571046077562880, respectively) with a new concept called the markaracter- and Q-conjugacy character tables, which enables us to discuss marks and characters for a finite group on a common basis of Q-conjugacy relationships between their cyclic subgroups. Then by using GAP (Groups, Algorithms and Programming) package we calculate all their dominant classes enabling us to find all possible Q-conjugacy characters for these sporadic groups. Finally, we prove in a main theorem that all twenty …