Jankogroup
In group theory, a Jankogroup is one of the four sporadic groups named after Zvonimir Janko . In 1965 Janko found the first Jankogroup J 1 and at the same time predicted the existence of Jankogroups J 2 and J 3 . In 1976 he then suspected the existence of the Jankogroup J 4 . Groups J 2 , J 3 , and J 4 were later proven by other mathematicians.
While the Jankogruppe J 2belongs to the so-called happy family , groups J 1 , J 3 and J 4 belong to the parias . This means that these three groups cannot be represented as subquotients ( quotient groups of subgroups ) of the monster group .
The four Jankogroups
- The Janko group J1 has the order 175 560 = 2 3 · 3 · 5 · 7 · 11 · 19. It is the only Janko group whose existence was proven by Janko himself.
- The Jankogroup J2 has the order 604 800 = 2 7 · 3 3 · 5 2 · 7. It was constructed by Marshall Hall and David Wales .
- The Janko group J3 has the order 50 232 960 = 2 7 * 3 5 * 5 * 17 * 19 and was constructed by Graham Higman and John McKay .
- The Jankogroup J4 has the order 86 775 571 046 077 562 880 = 2 21 · 3 3 · 5 · 7 · 11 3 · 23 · 29 · 31 · 37 · 43 and was constructed by Simon Norton .
Web links
- The sporadic groups in the Atlas of Finite Group Representations (English)