Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the number of circular orders on a group   We give a classification and complete algebraic description of groups
allowing only finitely many (left multiplication invariant) circular orders. In
particular, they are all solvable groups with a specific semi-direct product
decomposition. This allows us to also show that the space of circular orders of
any group is either finite or uncountable. As a special case and first step, we
show that the space of circular orderings of an infinite Abelian group has no
isolated points, hence is homeomorphic to a cantor set.

23
The categories of this paper are: solv-int
34
The categories of this paper are: chem-ph
25
The categories of this paper are: patt-sol
21
The categories of this paper are: adap-org
33
The categories of this paper are: plasm-ph
11
The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th
29
The categories of this paper are: funct-an
28
The categories of this paper are: alg-geom
22
The categories of this paper are: chao-dyn
17
The categories of this paper are: q-fin
7
The categories of this paper are: hep-th
8
The categories of this paper are: hep-ex
0
The categories of this paper are: hep-ph
12
The categories of this paper are: nucl-th
37
The categories of this paper are: supr-con