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 ℵ in which all subnormal subgroups of cardinality ℵ 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.
Uncountable groups in which normality is a transitive relation / De Falco, M.; de Giovanni, F.; Musella, C.; Sysak, Y. P.. - In: INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION. - ISSN 0218-1967. - 29:(2019), pp. 627-638.
Uncountable groups in which normality is a transitive relation
M. De Falco;F. de Giovanni;C. Musella;
2019
Abstract
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 ℵ in which all subnormal subgroups of cardinality ℵ 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.File in questo prodotto:
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