Let π be a free profinite group with free generators x_1, x_2 and let π' (resp. π") denote the commutator (resp. double-commutator) subgroup of π. Regard the full automorphism group A:= Aut(π) acting on the left of 7Γ. The purpose of this paper is to study some elementary arithmetic properties of a certain series of invariants Em: A × ~2 → (m ∈ N) reflecting the action of A on the meta-abelian quotient π/π". In particular, we shall introduce a canonical series of finite index subgroups of A fully exhausting congruity of the invariants E_m in a systematical way.
展开▼
