Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)


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
MathSciNet review: 0323907
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 20E15

Retrieve articles in all journals with MSC: 20E15

Additional Information

PII: S 0002-9947(1973)0323907-0
Keywords: Soluble group, transitive normality, proper homomorphic image
Article copyright: © Copyright 1973 American Mathematical Society