Tag Archives: Frattini subgroup

On the Frattini subgroup

Posted on 07/09/2020 by Peter Cameron

I wrote earlier about the Frattini subgroup of a group. It can be defined in either of two ways (as the set of non-generators of a group, the elements which can be dropped from any generating set containing them; or … Continue reading →

Posted in doing mathematics, exposition | Tagged , , | 5 Comments

Surprising fun fact

Posted on 06/09/2020 by Peter Cameron

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 →

Posted in doing mathematics | Tagged , | 2 Comments

The Frattini argument

Posted on 02/01/2020 by Peter Cameron

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 non-generators of G, that is, elements which … Continue reading →

Posted in exposition | Tagged , , | 5 Comments

Integrals of groups

Posted on 28/03/2018 by Peter Cameron

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 , , , | 2 Comments