## Groups whose homomorphic images have a transitive normality relation

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- by Derek J. S. Robinson PDF
- Trans. Amer. Math. Soc.
**176**(1973), 181-213 Request permission

## 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

- © Copyright 1973 American Mathematical Society
- 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