Janko group: Meaning (information, definition, explanation, facts)

In mathematics, the Janko groups J₁, J₂, J₃ and J₄ are four of the twenty-six sporadic groups; their respective orders are:

J1
J2
J3
J4

The Janko groups were first described by mathematician Zvonimir Janko in 1966; each of these groups has intricate matrix representations as maps into large general linear groups. For example, the matrix corresponding to J₄ gives a representation of J₄ in GL(112, 2).

References

• Zvonimir Janko, A new finite simple group with abelian Sylow subgroups and its characterization, Journal of Algebra 32:147-186, 1966