On orthogonal decomposition of homogeneous polynomials
In this paper we present a method of obtaining new examples of spaces of orderings by considering quotient structures of the space of orderings - it is, in general, nontrivial to determine whether, for a subgroup the derived quotient structure is a space of orderings, and we provide some insights into this problem. In particular, we show that if a quotient structure arising from a subgroup of index 2 is a space of orderings, then it necessarily is a profinite one.
In this paper, we first give several properties with respect to subgroups of self-similar groups in the sense of iterated function system (IFS). We then prove that some subgroups of -adic numbers are strong self-similar in the sense of IFS.