Geodesic
Isotype subgroups of mixed groups
Commentationes Mathematicae Universitatis Carolinae, Tome 42 (2001) no. 3, pp. 421-442
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In this paper, we initiate the study of various classes of isotype subgroups of global mixed groups. Our goal is to advance the theory of $\Sigma$-isotype subgroups to a level comparable to its status in the simpler contexts of torsion-free and $p$-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 $\Sigma$-isotype subgroups of such groups. This allows us to establish the fundamental fact that finite rank $\Sigma$-isotype subgroups of $k$-groups are themselves $k$-groups.
In this paper, we initiate the study of various classes of isotype subgroups of global mixed groups. Our goal is to advance the theory of $\Sigma$-isotype subgroups to a level comparable to its status in the simpler contexts of torsion-free and $p$-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 $\Sigma$-isotype subgroups of such groups. This allows us to establish the fundamental fact that finite rank $\Sigma$-isotype subgroups of $k$-groups are themselves $k$-groups.
Classification : 20K21, 20K27
Keywords: global $k$-group; $\Sigma$-isotype subgroup; $\ast$-isotype subgroup; knice subgroup; primitive element; $\ast$-valuated coproduct 
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     title = {Isotype subgroups of mixed groups},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {421--442},
     year = {2001},
     volume = {42},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_2001_42_3_a0/}
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Megibben, Charles; Ullery, William. Isotype subgroups of mixed groups. Commentationes Mathematicae Universitatis Carolinae, Tome 42 (2001) no. 3, pp. 421-442. http://geodesic.mathdoc.fr/item/CMUC_2001_42_3_a0/