## Fully transitive $p$-groups with finite first Ulm subgroup

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- by Agnes T. Paras and Lutz StrĂĽngmann PDF
- Proc. Amer. Math. Soc.
**131**(2003), 371-377 Request permission

## Abstract:

An abelian $p$-group $G$ is called (fully) transitive if for all $x,y\in G$ with $U_G(x)=U_G(y)$ ($U_G(x)\leq U_G(y)$) there exists an automorphism (endomorphism) of $G$ which maps $x$ onto $y$. It is a long-standing problem of A. L. S. Corner whether there exist non-transitive but fully transitive $p$-groups with finite first Ulm subgroup. In this paper we restrict ourselves to $p$-groups of type $A$, this is to say $p$-groups satisfying $\mathrm {Aut}(G)\upharpoonright _{ p^{\omega }G} = U(\mathrm {End}(G) \upharpoonright _{p^{\omega }G})$. We show that the answer to Cornerâ€™s question is no if $p^{\omega }G$ is finite and $G$ is of type $A$.## References

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## Additional Information

**Agnes T. Paras**- Affiliation: Department of Mathematics, University of the Philippines at Diliman, 1101 Quezon City, Philippines
- Email: agnes@math01.cs.upd.edu.ph
**Lutz StrĂĽngmann**- Affiliation: Fachbereich 6, Mathematik, University of Essen, 45117 Essen, Germany
- Email: lutz.struengmann@uni-essen.de
- Received by editor(s): August 9, 2001
- Received by editor(s) in revised form: September 27, 2001
- Published electronically: June 3, 2002
- Additional Notes: The first author was supported by project No. G-0545-173,06/97 of the
*German-Israeli Foundation for Scientific Research & Development*

The second author was supported by the Graduiertenkolleg*Theoretische und Experimentelle Methoden der Reinen Mathematik*of Essen University - Communicated by: Stephen D. Smith
- © Copyright 2002 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**131**(2003), 371-377 - MSC (2000): Primary 20K01, 20K10, 20K30
- DOI: https://doi.org/10.1090/S0002-9939-02-06593-0
- MathSciNet review: 1933327