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Uncountable groups in which normality is a transitive relation

    https://doi.org/10.1142/S0218196719500188Cited by:5 (Source: Crossref)

    A group is called a T-group if all its subnormal subgroups are normal. It is proved here that if G is an uncountable soluble periodic group of regular cardinality in which all subnormal subgroups of cardinality are normal, then G is a T-group, provided that it satisfies a suitable residual condition. An example shows that this latter restriction cannot be avoided.

    Communicated by A. Ol’shanskii

    AMSC: 20E15, 20E26
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