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sylow_counts

Function sylow_counts 

Source
pub fn sylow_counts(
    degree: usize,
    gens: &[Perm],
    cap: usize,
) -> Option<Vec<(u128, usize)>>
Expand description

The Sylow structure — for each prime p ∣ |G|, the number n_p of Sylow p-subgroups (the subgroups of maximal p-power order pᵃ ∥ |G|; all such subgroups are conjugate, so counting them counts the Sylow subgroups). Returned as (p, n_p) pairs sorted by p. Sylow’s theorems guarantee n_p ≡ 1 (mod p) and n_p ∣ |G|/pᵃ. None when the subgroup lattice is out of range.