On finitary series of groups represented as permutation or linear groups

Abstract

We mainly introduce finitary series of groups which can be represented as permutation or linear groups. Also we define (finitary permutation)-hypercentral (nilpotent) and (finitary linear)-hypercentral (nilpotent) groups. We give certain applications of the introduced concepts to perfect locally finite barely transitive p-groups.

Keywords:

• Finitary series
• finitary permutation
• cofinitary permutation
• linear groups
• minimal non-soluble groups
• minimal non-hypercentral groups
• barely transitive groups

2010 MATHEMATICS SUBJECT CLASSIFICATION::

• 20B07
• 20C32
• 20E25
• 20C99

Acknowledgement

The third author is grateful to Professor Ahmet Arikan and Professor Aynur Arikan for their kind hospitality, guidance and invitation to Gazi University.