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

Abstract

top
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 Σ -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 Σ -isotype subgroups of such groups. This allows us to establish the fundamental fact that finite rank Σ -isotype subgroups of k -groups are themselves k -groups.

How to cite

top

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 -

References

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

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.