Establishes closed all-rank formulas for P_r(G) in cyclic-index groups and F_q-Heisenberg families, plus rigidity and isoclinism determination from low-rank values.
Hall,The classification of prime-power groups, Journal f¨ ur die reine und angewandte Mathematik182(1940), 130–141
2 Pith papers cite this work. Polarity classification is still indexing.
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Pith papers citing it
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math.GR 2years
2026 2verdicts
UNVERDICTED 2representative citing papers
The number of homomorphisms from the free abelian group of rank r into a finite group G grows asymptotically as k * m^r, where m is the order of the largest abelian subgroup and k is the number of such subgroups.
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Higher Commutativity in Finite Groups, Rigidity, Extremal bounds, and Heisenberg-Type Families
Establishes closed all-rank formulas for P_r(G) in cyclic-index groups and F_q-Heisenberg families, plus rigidity and isoclinism determination from low-rank values.
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Higher Commutativity in Finite Groups: Exact Asymptotics and Finite Spectrum
The number of homomorphisms from the free abelian group of rank r into a finite group G grows asymptotically as k * m^r, where m is the order of the largest abelian subgroup and k is the number of such subgroups.