Moufang loops of small order. I
نویسندگان
چکیده
منابع مشابه
Moufang Loops of Small Order
The main result of this paper is the determination of all nonassociative Moufang loops of orders *31. Combinatorial type methods are used to consider a number of cases which lead to the discovery of 13 loops of the type in question and prove that there can be no others. All of the loops found are isomorphic to all of their loop isotopes, are solvable, and satisfy both Lagrange's theorem and Syl...
متن کامل0 N ov 1 99 6 CLASS 2 MOUFANG LOOPS , SMALL FRATTINI MOUFANG LOOPS , AND CODE LOOPS
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 ...
متن کاملThe Moufang loops of order 64 and 81
We classify Moufang loops of order 64 and 81 up to isomorphism, using a linear algebraic approach to central loop extensions. In addition to the 267 groups of order 64, there are 4262 nonassociative Moufang loops of order 64. In addition to the 15 groups of order 81, there are 5 nonassociative Moufang loops of order 81, 2 of which are commutative.
متن کاملToward the classification of Moufang loops of order 64
We show how to obtain all nonassociative Moufang loops of order less than 64 and 4262 nonassociative Moufang loops of order 64 in a unified way. We conjecture that there are no other nonassociative Moufang loops of order 64. The main idea of the computer search is to modify precisely one quarter of the multiplication table in a certain way, previously applied to small
متن کاملMoufang Loops of Order 2 m , m odd
We first show that every Moufang loop L which contains an abelian associative subloop M of index two and odd order must, in fact, be a group. We then use this to settle the question ”For what value of n = 2m, m odd, must a Moufang loop of order n be associative?” Introduction: This paper is motivated by a question asked by Rajah and Jamal in [19]: If L is a Moufang loop of order 2m with an abel...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1974
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-1974-0330336-3