proof of the Burnside basis theorem
Let be a -group and its Frattini subgroup.
Now both and are characteristic subgroups of so in particular is normal in . If we pass to we find that is abelian and every element has order – that is, is a vector space over . So the maximal subgroups of are in a 1-1 correspondence with the hyperplanes of . As the intersection of all hyperplanes of a vector space is the origin, it follows the intersection of all maximal subgroups of is . That is, .
|Title||proof of the Burnside basis theorem|
|Date of creation||2013-03-22 15:46:25|
|Last modified on||2013-03-22 15:46:25|
|Last modified by||Algeboy (12884)|