Some New Results for the Square Subgroup of an Abelian Group

Abstract

The complete description of the square subgroup of a torsion abelian group and an elementary construction of a mixed abelian group (A, +, 0), such that the quotient group of A modulo the square subgroup □A is not a nil-group, are given (also for the associative case). Some A. M. Aghdam's results concerning square subgroups for the associative case are proven. The relationship between square subgroups for both the cases of associative and general rings is partially investigated.

Key Words:

• Associative ring multiplication
• nil-groups

2010 Mathematics Subject Classification:

• Primary: 20K99
• Secondary: 16B99