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Analysis of Metabolic Differences and Core Regulatory Pathways in Lactic Acid Bacteria-Fermented Broths of Different <i>Ziziphus jujuba</i> Mill. Varieties Based on LC-MS Untargeted Metabolomics. [PDF]
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Unification in Varieties of Groups: Nilpotent Varieties
Canadian Journal of Mathematics, 1994Abstract In this paper we show that any system of equations over a free nilpotent group of class c is either unitary or miliary. In fact, such a system either has a most general solution (akin to the most general solution of a system of linear dipohantine equations), or every solution
Albert, Michael H., Lawrence, John
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The main result of the paper under review is the following: Theorem 1.5. For any positive integers \(k\) and \(n\) there exists \(t\) depending only on \(k\) and \(n\) such that the class of all groups \(G\) satisfying the identity \(w_t^n\equiv 1\) and having \(\gamma_k(G)\) locally finite is a variety, where the symbol \(w_j\) denotes a word that is ...
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VARIETIES OF GROUP REPRESENTATIONS
Russian Mathematical Surveys, 1977A group representation is a pair (A,Γ), where A is a module over a commutative ring K with identity and Γ is a group that acts on A. In the category of group representations over a fixed K, both A and Γ are variable. We study varieties in this category. This paper is a survey of results and problems in this area and connections with other topics.
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On Metanilpotent Varieties of Groups
Canadian Journal of Mathematics, 1970Let denote the variety of all groups which are extensions of a nilpotent-of-class-c group by a nilpotent-of-class-d group, and let denote the variety of all metabelian groups. The main result of this paper is the following theorem.THEOREM. Let be a subvariety of which does not contain .
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