Some Skew Linear Groups Satisfying Generalized Group Identities

Abstract

In this article, we consider a type of generalized group identity and extend some earlier results. For example, we show that, if D is a division ring with infinite center, then every subnormal subgroup of GL_n(D) satisfying a generalized group identity over GL_n(D) is central.

Key Words:

• Division ring
• Engel group
• Generalized group identity
• Linear group
• Subnormal subgroup

2010 Mathematics Subject Classification:

• 16K20
• 16K99
• 20F10