Abstract 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. For example, a complete characterization of those valuated groups H that are universally fully transitive in the sense that every group G that contains H as such an embedded subgroup is necessarily H-fully transitive. Particular attention is given to the case where H is isotype in G, so the induced valuation agrees with the height valuation on H. Our results concerning the full transitivity of Abelian p-groups somewhat enlarge those obtained by Griffith (1968) [9] and Goldsmith and Strungmann (2007) [8] . Our other results concerning the valuated Abelian p-groups somewhat refine those established by Richman and Walker (1979) [17] .

中文翻译：

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完全可传递和可估价的阿贝尔 p 群的推广

摘要 如果 H 是阿贝尔 p 群 G 的子群，如果使用来自 G 的高度估值，我们说 G 是 H-完全可传递的，对于每个 x ∈ H ，每个估值（即非高度递减）同态 〈 x 〉 → G 扩展到一个有值的同态 H → G 。这个概念是卡普兰斯基对完全传递群的经典定义的概括。建立了这个想法的许多有趣的特性。例如，在每个包含 H 作为嵌入子群的群 G 必然是 H-完全可传递的意义上，这些被赋值的群 H 的完整表征是普遍完全可传递的。特别注意H在G中是同种型的情况，因此诱导估值与H的高度估值一致。我们关于阿贝尔 p 群完全传递性的结果在某种程度上扩大了 Griffith (1968) [9] 和 Goldsmith 和 Strungmann (2007) [8] 获得的结果。我们关于评估的阿贝尔 p 群的其他结果在某种程度上改进了 Richman 和 Walker (1979) [17] 建立的结果。