RO EN
On Frattini subloops and normalizers of commutative Moufang loop
Authors: N. I. Sandu
Keywords: Commutative Moufang loop, multiplication group, Frattini subloop, Frattini subgroup, normalizer, loop with normalizer condition, divisible loop.
– 0.20 Mb
Keywords: Commutative Moufang loop, multiplication group, Frattini subloop, Frattini subgroup, normalizer, loop with normalizer condition, divisible loop.
Abstract
Let $L$ be a commutative Moufang loop (CML) with the multiplication group $\frak M$, and let $\frak F(L)$, $\frak F(\frak M)$ be the Frattini subloop of $L$ and Frattini subgroup of $\frak M$. It is proved that $\frak F(L) = L$ if and only if $\frak F(\frak M) = \frak M$, and the structure of this CML is described. The notion of normalizer for subloops in CML is defined constructively. 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 $\frak M$.N. I. Sandu
Tiraspol State University
str. Iablochkin, 5, Chisinau, MD-2069
Moldova
E-mail:
Tiraspol State University
str. Iablochkin, 5, Chisinau, MD-2069
Moldova
E-mail:
Fulltext
– 0.20 Mb
Contents
- Boundedness for Vector-Valued Multilinear Singular Integral Operator on Lp Spaces with Variable Exponent
- On Frattini subloops and normalizers of commutative Moufang loop
- On a Method for Estimation of Risk Premiums Loaded by a Fraction of the Variance of the Risk
- Properties of covers in the lattice of group topologies for nilpotent groups
- A Note on the Affine Subspaces of Three-Dimensional Lie Algebras
- Solving the games generated by the informational extended strategies of the players
- Stability analysis of Pareto optimal portfolio of multicriteria investment maximin problem in the Hölder metric
- Invariant transformations of loop transversals. 2. The case of isotopy
