Single axioms for odd exponent groups
نویسندگان
چکیده
منابع مشابه
The Shortest Single Axioms for Groups of Exponent 4
We study equations of the form (= x) which are single axioms for groups of exponent 4, where is a term in product only. Every such must have at least 9 variable occurrences, and there are exactly three such of this size, up to variable renaming and mirroring. These terms were found by an exhaustive search through all terms of this form. Automated techniques were used in two ways: to eliminate m...
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We present new results in axiomatic group theory obtained by using automated deduction programs. The results include single axioms, some with the identity and others without, for groups of exponents 3, 4, 5, and 7, and a general form for single axioms for groups of odd exponent. The results were obtained by using the programs in three separate ways: as a symbolic calculator, to search for proof...
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We study amalgams and the strong, weak, and special amalgamation bases in the varieties of nilpotent groups of class two and exponent n, where n is odd. The main result is the characterization of the special amalgamation bases for these varieties. We also characterize the weak and strong bases. For special amalgamation bases we show that there are groups which are special bases in varieties of ...
متن کاملSingle Implicative Axioms for Groups and for Abelian Groups
Groups are usually deened by means of three axioms|the associative law, the existence of an identity element, and the existence of an inverse to each element. For abelian groups, the commutative law is included as a fourth axiom. However, it is well known that groups (also abelian groups) can be deened with a single equation. In 7], Tarski presented the single axiom x ? (y ? (z ? (x ? y))) = z ...
متن کاملOn Subgroups of Free Burnside Groups of Large Odd Exponent
We prove that every noncyclic subgroup of a free m-generator Burnside group B(m, n) of odd exponent n ≫ 1 contains a subgroup H isomorphic to a free Burnside group B(∞, n) of exponent n and countably infinite rank such that for every normal subgroup K of H the normal closure 〈K〉B(m,n) of K in B(m, n) meets H in K. This implies that every noncyclic subgroup of B(m, n) is SQ-universal in the clas...
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ژورنال
عنوان ژورنال: Journal of Automated Reasoning
سال: 1995
ISSN: 0168-7433,1573-0670
DOI: 10.1007/bf00881714