Affordable Access

Publisher Website

XIV Mixed Groups

Elsevier B.V.
DOI: 10.1016/s0079-8169(08)62775-0
  • Mathematics


Publisher Summary The mixed groups A form the most general class of abelian groups and a satisfactory structure theory must provide full information about their torsion parts T and the corresponding torsion-free group A/T, and at the same time describe the way in which these groups are put together to form A. Therefore, such a theory can be expected only for those classes of mixed groups A for which both T and A/T can be characterized in a satisfactory way. Then, the problem reduces to finding tools by means of which the nonisomorphic extensions of T by A/T can be described. The height-matrices discussed in the chapter are adequate for several groups of torsion-free rank I. A great deal of work has been done on the splitting problem—that is, when the mixed group splits into the direct sum of its torsion part and a torsion-free group. The chapter describes all torsion groups T and all torsion-free groups G, respectively, such that every mixed group splits whose torsion part is isomorphic to T and whose quotient mod its torsion part is isomorphic to G, respectively. The chapter also explains the construction of groups with given Ulm sequences. A rather intricate procedure leads to an existence theorem that is useful in establishing the existence of groups with certain properties.

There are no comments yet on this publication. Be the first to share your thoughts.


Seen <100 times

More articles like this

Ternary complexes in solution. XIV. The stability...

on Zeitschrift für Naturforschun... November 1972
More articles like this..