On Gap Conjecture concerning group growth

Details On Gap Conjecture concerning group growth On Gap Conjecture concerning group growth

2012-02-27

arxiv.org/abs/1202.6044v1

Mathematics

Group Theory

Scientific paper

We discuss some new results concerning the Gap Conjecture on group growth and present a reduction of the Gap Conjecture to several special classes of groups. Namely we show that its validity for the classes of simple groups and residually finite groups will imply the Gap Conjecture in full generality. A similar type reduction holds if the Conjecture is valid for residually polycyclic groups and just-infinite groups. The cases of residually solvable groups and right orderable groups are considered as well.

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