D-property for a prime set

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Template:Prime set-parametrized group property

Definition

Let G be a finite group, and \pi be a set of primes. We say that G satisfies D_\pi if D has a \pi-Hall subgroup H (viz, a Hall subgroup whose order contains only primes from \pi and whose index contains no primes from \pi) and every \pi-subgroup (subgroup whose order contains only primes from \pi) is contained in a conjugate of H.

The D here stands for Domination and relates to the problem of whether we can extend Sylow's theorems to Hall subgroups.

Relation with other properties

Weaker properties