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 non-generators of a group, the elements which can be dropped from any generating set containing them; or … Continue reading

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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

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

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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

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