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The generalized criterion of Dieudonné for valuated p -groups

Peter Vassilev Danchev (2006)

Acta Mathematica Universitatis Ostraviensis

We prove that if G is an abelian p -group with a nice subgroup A so that G / A is a Σ -group, then G is a Σ -group if and only if A is a Σ -subgroup in G provided that A is equipped with a valuation induced by the restricted height function on G . In particular, if in addition A is pure in G , G is a Σ -group precisely when A is a Σ -group. This extends the classical Dieudonné criterion (Portugal. Math., 1952) as well as it supplies our recent results in (Arch. Math. Brno, 2005), (Bull. Math. Soc. Sc. Math....

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