Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nuclear properties of loop extensions   The objectives of this paper is to give a systematic investigation of
extension theory of loops. A loop extension is (left, right or middle) nuclear,
if the kernel of the extension consists of elements associating (from left,
right or middle) with all elements of the loop. It turns out that the natural
non-associative generalizations of the Schreier's theory of group extensions
can be characterized by different types of nuclear properties. Our loop
constructions are illustrated by rich families of examples in important loop
classes.

27
The categories of this paper are: comp-gas
8
The categories of this paper are: hep-ex
24
The categories of this paper are: dg-ga
31
The categories of this paper are: ao-sci
15
The categories of this paper are: nucl-ex
35
The categories of this paper are: mtrl-th
21
The categories of this paper are: adap-org
33
The categories of this paper are: plasm-ph
20
The categories of this paper are: acc-phys
5
The categories of this paper are: gr-qc
34
The categories of this paper are: chem-ph
11
The categories of this paper are: hep-lat
22
The categories of this paper are: chao-dyn
25
The categories of this paper are: patt-sol
26
The categories of this paper are: bayes-an
16
The categories of this paper are: stat