Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Extensions of groups by weighted Steiner loops   Solving functional equations given in \cite{nagy} for extensions of a group
$A$ by a weighted Steiner loop $S$ we obtain concrete description for all loops
with interesting weak associativity properties if the Steiner loop $S$ induces
only the trivial automorphism on $A$. We show that the restricted Fischer
groups and their geometry play an important role for loop extension with right
alternative property. Also the automorphism groups of these extensions as well
as the conditions for isomorphisms between two extensions are studied.

23
The categories of this paper are: solv-int
27
The categories of this paper are: comp-gas
8
The categories of this paper are: hep-ex
19
The categories of this paper are: eess
20
The categories of this paper are: acc-phys
35
The categories of this paper are: mtrl-th
21
The categories of this paper are: adap-org
1
The categories of this paper are: cs
12
The categories of this paper are: nucl-th
14
The categories of this paper are: math-ph
6
The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci
17
The categories of this paper are: q-fin
37
The categories of this paper are: supr-con
36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics