Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On topologizable and non-topologizable groups   A group $G$ is called hereditarily non-topologizable if, for every $H\le G$,
no quotient of $H$ admits a non-discrete Hausdorff topology. We construct first
examples of infinite hereditarily non-topologizable groups. This allows us to
prove that c-compactness does not imply compactness for topological groups. We
also answer several other open questions about c-compact groups asked by
Dikranjan and Uspenskij. On the other hand, we suggest a method of constructing
topologizable groups based on generic properties in the space of marked
$k$-generated groups. As an application, we show that there exist non-discrete
quasi-cyclic groups of finite exponent; this answers a question of Morris and
Obraztsov.

27
The categories of this paper are: comp-gas
1
The categories of this paper are: cs
9
The categories of this paper are: nlin
19
The categories of this paper are: eess
36
The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph
3
The categories of this paper are: physics
37
The categories of this paper are: supr-con
6
The categories of this paper are: astro-ph
32
The categories of this paper are: atom-ph
21
The categories of this paper are: adap-org
35
The categories of this paper are: mtrl-th
15
The categories of this paper are: nucl-ex
10
The categories of this paper are: q-bio
12
The categories of this paper are: nucl-th
17
The categories of this paper are: q-fin