Solvable normal subgroups of 2-knot groups

被引:0
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作者
Hillman, J. A. [1 ]
机构
[1] Univ Sydney, Sch Math & Stat, Sydney, NSW 2006, Australia
关键词
Center; Hirsch-Plotkin radical; 2-knot; solvable; surgery; torsion; FINITE; KNOT;
D O I
10.1142/S0218216517500663
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
If X is an orientable, strongly minimal PD4-complex and pi(1)(X) has one end, then it has no nontrivial locally finite normal subgroup. Hence, if pi is a 2-knot group, then (a) if pi is virtually solvable, then either pi has two ends or p congruent to Phi, with presentation < a, t|ta = a(2)t >, or pi is torsion-free and polycyclic of Hirsch length 4 (b) either pi has two ends, or pi has one end and the center zeta pi is torsion-free, or pi has infinitely many ends and zeta pi is finite, and (c) the Hirsch-Plotkin radical root pi is nilpotent.
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页数:11
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