Fee subgroup

A fee subgroup \(H\) of a linearly ordered subgroup \(G\)is a subgroup such that \(g^{-1}Hg \subset H\) for all \(g > 1\).

When \(G\) is bi-ordered, and \(a(g) = a(h)\) implies \(a(fg) = a(fh)\) and \(a(gf) = a(hf)\) for all \(f > 1\), \(P(a) = \{g^{-1}h \mid a(g) = a(h)\}\) is a fee subgroup.

A fee subgroup is not always normal .