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On commutative Moufang loops with some restrictions for subgroups of its multiplication groups

N. T. Lupashco

Tiraspol State University, Chişinău, Moldova

Abstract: Let $\mathfrak M$ be the multiplication group of a commutative Moufang loop $Q$. In this paper it is proved that if all infinite abelian subgroups of $\mathfrak M$ are normal in $\mathfrak M$, then $Q$ is associative. If all infinite nonabelian subgroups of $\mathfrak M$ are normal in $\mathfrak M$, then all nonassociative subloops of $Q$ are normal in $Q$, all nonabelian subgroups of $\frak M$ are normal in $\mathfrak M$ and the commutator subgroup $\mathfrak M'$ is a finite 3-group.

Keywords and phrases: Commutative Moufang loop, minimum condition, multiplication $IH$-group, multiplication $\overline{IH}$-group, metahamiltonian group.

MSC: 20N05

Received: 05.06.2006

Language: English

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