Groups whose factor group modulo the upper hypercenter is of finite 0-rank

Abstract

The authors prove that if G is a group such that $G/{\zeta }_{\infty }(G)$ has finite 0-rank r and if every periodic factor group of G is locally finite, then G contains a normal subgroup K of finite 0-rank at most $r(5r^2+5r+1)/2$ such that G/K is a torsion-free hypercentral group.

Keywords:

• Finite special rank
• section p-rank
• torsion-free rank
• upper hypercenter
• 0-rank

2010 Mathematics Subject Classification:

• Primary: 20E15
• Secondary 20E25
• 20F50