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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

On the join of subnormal subgroups


Author: A. J. Van Werkhooven
Journal: Proc. Amer. Math. Soc. 42 (1974), 1-7
MSC: Primary 20F30
DOI: https://doi.org/10.1090/S0002-9939-1974-0335650-9
MathSciNet review: 0335650
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Abstract: Let $ \mathfrak{G}$ be the class of finitely generated groups. If the join of finitely many subnormal $ \mathfrak{X} = sn\mathfrak{X}$ subgroups is always an $ \mathfrak{X}$-group and $ \mathfrak{N} = \{ sn,q,{n_0}\} \mathfrak{N} \subseteq \mathfrak{G}$, then the join of finitely many subnormal $ \mathfrak{X}\mathfrak{N}$-subgroups is an $ \mathfrak{X}\mathfrak{N}$-group. If the subnormal coalition class $ \mathfrak{X}$ and the class $ \mathfrak{N} = \{ sn,q,{n_0}\} \mathfrak{N}$ are such that whenever $ A \in \mathfrak{X}\mathfrak{N}$, A has a maximum subnormal $ \mathfrak{X}$-subgroup, then $ \mathfrak{X}(\mathfrak{N} \wedge \mathfrak{G})$ is a subnormal coalition class $ (\mathfrak{N} \wedge \mathfrak{G}$ is the class of finitely generated $ \mathfrak{N}$-groups).


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DOI: https://doi.org/10.1090/S0002-9939-1974-0335650-9
Keywords: Subnormal, subnormal coalition class
Article copyright: © Copyright 1974 American Mathematical Society

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