Groups whose subnormal subgroups have finite normal oscillation

ABSTRACT

If X is a subgroup of a group G, the cardinal number $min\left\{\right|X:X_G|,|X^G:X\left|\right\}$ is called the normal oscillation of X in G. The structure of soluble groups in which all subnormal subgroups have finite normal oscillation is investigated here, taking as a model the known theory of T-groups, i.e., groups in which normality is a transitive relation.

KEYWORDS:

• Normal oscillation
• subnormal subgroup
• T-group

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• 20E15

Acknowledgment

The authors are members of GNSAGA (INdAM) and work within the A_DV-AGTA project.