On the join of subnormal subgroups
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- by A. J. Van Werkhooven PDF
- Proc. Amer. Math. Soc. 42 (1974), 1-7 Request permission
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).References
- Derek J. S. Robinson, Infinite soluble and nilpotent groups, Queen Mary College Mathematics Notes, Queen Mary College, London, 1967. MR 0269740
- Derek S. Robinson, Joins of subnormal subgroups, Illinois J. Math. 9 (1965), 144–168. MR 170953
- J. E. Roseblade and S. E. Stonehewer, Subjunctive and locally coalescent classes of groups, J. Algebra 8 (1968), 423–435. MR 222156, DOI 10.1016/0021-8693(68)90053-7
- S. E. Stonehewer, The join of finitely many subnormal subgroups, Bull. London Math. Soc. 2 (1970), 77–82. MR 257226, DOI 10.1112/blms/2.1.77
Additional Information
- © Copyright 1974 American Mathematical Society
- 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