Megibben, Charles K., and Ullery, William. "Isotype subgroups of mixed groups." Commentationes Mathematicae Universitatis Carolinae 42.3 (2001): 421-442. <http://eudml.org/doc/22572>.
@article{Megibben2001,
abstract = {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.},
author = {Megibben, Charles K., Ullery, William},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {global $k$-group; $\Sigma $-isotype subgroup; $\ast $-isotype subgroup; knice subgroup; primitive element; $\ast $-valuated coproduct; mixed Abelian groups; global Warfield groups; covers; simply presented groups; strongly separable subgroups; almost balanced pure subgroups; isotype subgroups; pure knice subgroups},
language = {eng},
number = {3},
pages = {421-442},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Isotype subgroups of mixed groups},
url = {http://eudml.org/doc/22572},
volume = {42},
year = {2001},
}
TY - JOUR
AU - Megibben, Charles K.
AU - Ullery, William
TI - Isotype subgroups of mixed groups
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2001
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 42
IS - 3
SP - 421
EP - 442
AB - 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.
LA - eng
KW - global $k$-group; $\Sigma $-isotype subgroup; $\ast $-isotype subgroup; knice subgroup; primitive element; $\ast $-valuated coproduct; mixed Abelian groups; global Warfield groups; covers; simply presented groups; strongly separable subgroups; almost balanced pure subgroups; isotype subgroups; pure knice subgroups
UR - http://eudml.org/doc/22572
ER -
