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 six simple sporadic groups are unmatured.
Study on the Q-Conjugacy Relations for the Janko Groups,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 11,
2, Article 29.
Available at: https://digitalcommons.pvamu.edu/aam/vol11/iss2/29