# Isotype subgroups of mixed groups

Charles K. Megibben; William Ullery

Commentationes Mathematicae Universitatis Carolinae (2001)

- Volume: 42, Issue: 3, page 421-442
- ISSN: 0010-2628

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topMegibben, 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 -

## References

top- Hill P., Megibben C., Torsion free groups, Trans. Amer. Math. Soc. 295 (1986), 735-751. (1986) Zbl0597.20047MR0833706
- Hill P., Megibben C., Knice subgroups of mixed groups, Abelian Group Theory Gordon-Breach New York (1987), 89-109. (1987) Zbl0653.20057MR1011306
- Hill P., Megibben C., Pure subgroups of torsion-free groups, Trans. Amer. Math. Soc. 303 (1987), 765-778. (1987) Zbl0627.20028MR0902797
- Hill P., Megibben C., Mixed groups, Trans. Amer. Math. Soc. 334 (1992), 121-142. (1992) Zbl0798.20050MR1116315
- Hill P., Megibben C., Ullery W., $\Sigma $-isotype subgroups of local $k$-groups, Contemp. Math. 273 (2001), 159-176. (2001) Zbl0982.20038MR1817160

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