Let be a finite group with order , and let be a prime integer. We can write for some integers, such that and are coprimes (that is, is the highest power of that divides ). Any subgroup of whose order is is called a Sylow -subgroup.
While there is no reason for Sylow -subgroups to exist for any finite group, the fact is that all groups have Sylow -subgroups for every prime that divides . This statement is the First Sylow theorem
When we simply say that is a -group.
|Date of creation||2013-03-22 14:02:14|
|Last modified on||2013-03-22 14:02:14|
|Last modified by||drini (3)|