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Transactions of the American Mathematical Society

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Groups whose homomorphic images have a transitive normality relation


Author: Derek J. S. Robinson
Journal: Trans. Amer. Math. Soc. 176 (1973), 181-213
MSC: Primary 20E15
DOI: https://doi.org/10.1090/S0002-9947-1973-0323907-0
MathSciNet review: 0323907
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Abstract: A group G is a T-group if $ H \triangleleft K \triangleleft G$ implies that $ H \triangleleft G$, i.e. normality is transitive. A just non-T-group (JNT-group) is a group which is not a T-group but all of whose proper homomorphic images are T-groups. In this paper all soluble JNT-groups are classified; it turns out that these fall into nine distinct classes. In addition all soluble $ JN\bar T$-groups and all finite $ JN\bar T$-groups are determined; here a group G is a $ \bar T$-group if $ H \triangleleft K \triangleleft L \leq G$ implies that $ H \triangleleft L$. It is also shown that a finitely generated soluble group which is not a T-group has a finite homomorphic image which is not a T-group.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1973-0323907-0
Keywords: Soluble group, transitive normality, proper homomorphic image
Article copyright: © Copyright 1973 American Mathematical Society

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