Generalizations of fully transitive and valuated Abelian p-groups A. R. Chekhlov, P. V. Danchev, P. W. Keef
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ArticleContent type: Текст Media type: электронный Subject(s): вполне транзитивные группы | транзитивные абелевы группы | абелевы группы | гомоморфизмGenre/Form: статьи в журналах Online resources: Click here to access online
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Journal of algebra Vol. 566. P. 187-204Abstract: If H is a subgroup of an Abelian p-group G, we say G is H-fully transitive if using the height valuation from G, for every x ∈ H, every valuated (i.e., non-height decreasing) homomorphism x → G extends to a valuated homomorphism H → G. This notion is a generalization of the classical definition of fully transitive groups due to Kaplansky. A number of interesting properties of this idea are established.
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If H is a subgroup of an Abelian p-group G, we say G is H-fully transitive if using the height valuation from G, for every x ∈ H, every valuated (i.e., non-height decreasing) homomorphism x → G extends to a valuated homomorphism H → G. This notion is a generalization of the classical definition of fully transitive groups due to Kaplansky. A number of interesting properties of this idea are established.
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