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Charles Megibben, William Ullery 1IJOFA IK>CHKFI B ENA@ CHKFI

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Charles Megibben, William Ullery Isotype subgroups of mixed groups

Comment.Math.Univ.Carolinae 42,3 (2001) 421-442.

Abstract: In this paper, we initiate the study of various classes of isotype sub- groups of global mixed groups. Our goal is to advance the theory of Σ-isotype subgroups to a level comparable to its status in the simpler contexts of torsion- free andp-local mixed groups. Given the history of those theories, one anticipates that definitive results are to be found only when attention is restricted to global k-groups, the prototype being global groups with decomposition bases. A large portion of this paper is devoted to showing that primitive elements proliferate in Σ-isotype subgroups of such groups. This allows us to establish the fundamental fact that finite rank Σ-isotype subgroups ofk-groups are themselvesk-groups.

Keywords: global k-group, Σ-isotype subgroup, ∗-isotype subgroup, knice sub- group, primitive element,∗-valuated coproduct

AMS Subject Classification: 20K21, 20K27

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