Most small $${\varvec{p}}$$ p -groups have an automorphism of order 2

We generalize the common notion of descending and ascending central series. The descending approach determines a naturally graded Lie ring and the ascending version determines a graded module for this ring. We also link derivations of these rings to the automorphisms of a group. This process uncovers new structure in 4/5 of the approximately 11.8 million groups of size at most 1000 and beyond that point pertains to at least a positive logarithmic proportion of all finite groups.

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Most small $${\varvec{p}}$$ p -groups have an automorphism of order 2

Cited by 2 publications

References 9 publications

Filters compatible with isomorphism testing

Filters compatible with isomorphism testing

New Lie products for groups and their automorphisms

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