Hall triple systems and commutative Moufang exponent 3 loops: The case of nilpotence class 2
نویسندگان
چکیده
منابع مشابه
A shortest single axiom with neutral element for commutative Moufang loops of exponent 3
In this brief note, we exhibit a shortest single product and neutral element axiom for commutative Moufang loops of exponent 3 that was found with the aid of the automated theorem-prover Prover9.
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Let L be a Moufang loop which is centrally nilpotent of class 2. We first show that the nuclearly-derived subloop (normal associator subloop) L∗ of L has exponent dividing 6. It follows that Lp (the subloop of L of elements of p-power order) is associative for p > 3. Next, a loop L is said to be a small Frattini Moufang loop, or SFML, if L has a central subgroup Z of order p such that C ∼= L/Z ...
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The structure of the commutative Moufang loops (CML) with minimum condition for subloops is examined. In particular it is proved that such a CML Q is a finite extension of a direct product of a finite number of the quasicyclic groups, lying in the centre of the CML Q. It is shown that the minimum conditions for subloops and for normal subloops are equivalent in a CML. Moreover, such CML also ch...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 1984
ISSN: 0097-3165
DOI: 10.1016/0097-3165(84)90001-3