Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Group Structures on Families of Subsets of a Group   A binary operation on any set induces a binary operation on its subsets. We
explore families of subsets of a group that become a group under the induced
operation and refer to such families as power groups of the given group. Our
results serve to characterize some types of groups in terms of their power
groups. In particular, we consider when the only power groups of a group are
the factor groups of its subgroups and when that is the case up to isomorphism.
We prove that the former are precisely those groups for which every element has
finite order and provide examples to illustrate that the latter is not always
the case. In the process we consider several natural questions such as whether
the identity element of the group must belong to the identity element of a
power group or the inverse of an element in a power group must consist of the
inverses of its elements.

31
The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat
7
The categories of this paper are: hep-th
33
The categories of this paper are: plasm-ph
6
The categories of this paper are: astro-ph
20
The categories of this paper are: acc-phys
35
The categories of this paper are: mtrl-th
32
The categories of this paper are: atom-ph
24
The categories of this paper are: dg-ga
17
The categories of this paper are: q-fin
19
The categories of this paper are: eess
12
The categories of this paper are: nucl-th
9
The categories of this paper are: nlin
30
The categories of this paper are: q-alg
13
The categories of this paper are: quant-ph
22
The categories of this paper are: chao-dyn