Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Frattini subloops and normalizers of commutative Moufang loops   Let $L$ be a commutative Moufang loop (CML) with multiplication group $\frak
M$, and let $\frak F(L)$, $\frak F(\frak M)$ be the Frattini subgroup and
Frattini subgroup of $L$ and $\frak M$ respectively. It is proved that $\frak
F(L) = L$ if and only if $\frak F(\frak M) = \frak M$ and is described the
structure of this CLM. Constructively it is defined the notion of normalizer
for subloops in CML. Using this it is proved that if $\frak F(L) \neq L$ then
$L$ satisfies the normalizer condition and that any divisible subgroup of
$\frak M$ is an abelian group and serves as a direct factor for $\frak M$.

3
The categories of this paper are: physics
21
The categories of this paper are: adap-org
0
The categories of this paper are: hep-ph
14
The categories of this paper are: math-ph
12
The categories of this paper are: nucl-th
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
15
The categories of this paper are: nucl-ex
36
The categories of this paper are: cmp-lg
27
The categories of this paper are: comp-gas
33
The categories of this paper are: plasm-ph
6
The categories of this paper are: astro-ph
35
The categories of this paper are: mtrl-th
37
The categories of this paper are: supr-con
23
The categories of this paper are: solv-int