Vol. 37(51), pp. 5760 (1985) 

S.J. PrideDepartment of Mathematics, University of Glasgow, G128QW, ScotlandAbstract: In previous papers the autor has defined a quasiorder $\preceq$ on the class of groups (the``largeness'' ordering). One can then define the {\it height\/} of group, and also define what it means for a group to satisfy max$\preceq$ or min$\preceq$. A natural question is whether the finiteness conditions max$\preceq$, min$\preceq$, ``having finite height'' are extension closed. It is shown here that the answer is ``no'' for all three properties: there is a group which is a split extension of one group of height 1 by another group of height 1, and which does not satisfy max$\preceq$ or min$\preceq$. Classification (MSC2000): 20F22; 20E22 Full text of the article:
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© 2001 Mathematical Institute of the Serbian Academy of Science and Arts
