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Tag Archives: Frattini subgroup
On the Frattini subgroup
I wrote earlier about the Frattini subgroup of a group. It can be defined in either of two ways (as the set of nongenerators of a group, the elements which can be dropped from any generating set containing them; or … Continue reading
Posted in doing mathematics, exposition
Tagged Frattini subgroup, G. A. Miller, writing mathematics
5 Comments
Surprising fun fact
I have just found a proof of the following. Usual caveat: nobody else has read the proof yet, and I have not carefully checked it. Let G be a finite group. The finite group H will be called an inverse … Continue reading
The Frattini argument
The Frattini subgroup of a finite group G can be defined in two equivalent ways: it is the intersection of all the maximal proper subgroups of G; it is the set of all nongenerators of G, that is, elements which … Continue reading
Integrals of groups
Everyone who has studied mathematics knows what the derivative and integral of a function are. The derivative measures rate of change, the integral (the inverse operation) measures area under a curve. They are inverse operations; and two functions have the … Continue reading
Posted in doing mathematics, exposition
Tagged abelian group, derived subgroup, Frattini subgroup, inverse group theory
2 Comments