Realizing automorphism groups of metabelian groups

GLn and the automorphism groups of free metabelian groups and polynomial rings

Groups - St Andrews 1981 ◽

10.1017/cbo9780511661884.009 ◽

1982 ◽

pp. 160-168

Author(s):

S. Bachmuth ◽

H.Y. Mochizuki

Keyword(s):

Automorphism Groups ◽

Polynomial Rings ◽

Metabelian Groups

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Outer automorphism groups of metabelian groups

Journal of Pure and Applied Algebra ◽

10.1016/s0022-4049(99)00022-5 ◽

2000 ◽

Vol 149 (3) ◽

pp. 251-266 ◽

Cited By ~ 9

Author(s):

Rüdiger Göbel ◽

Agnes T. Paras

Keyword(s):

Automorphism Groups ◽

Outer Automorphism ◽

Metabelian Groups ◽

Outer Automorphism Groups

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Automorphism groups of metabelian groups

Mathematical Notes ◽

10.1007/bf01159522 ◽

1987 ◽

Vol 41 (1) ◽

pp. 7-14 ◽

Cited By ~ 1

Author(s):

G. A. Noskov

Keyword(s):

Automorphism Groups ◽

Metabelian Groups

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Automorphism Groups of Two Generator Metabelian Groups

Journal of the London Mathematical Society ◽

10.1112/jlms/s2-36.3.393 ◽

1987 ◽

Vol s2-36 (3) ◽

pp. 393-406 ◽

Cited By ~ 6

Author(s):

S. Bachmuth ◽

G. Baumslag ◽

J. Dyer ◽

H. Y. Mochizuki

Keyword(s):

Automorphism Groups ◽

Metabelian Groups

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Representations of holomorphs of group extensions with Abelian kernels

Mathematical Proceedings of the Cambridge Philosophical Society ◽

10.1017/s0305004100051835 ◽

1975 ◽

Vol 78 (3) ◽

pp. 357-368 ◽

Cited By ~ 3

Author(s):

B. A. F. Wehrfritz

Keyword(s):

Abelian Group ◽

Automorphism Group ◽

Finite Rank ◽

Automorphism Groups ◽

Abelian Groups ◽

Finitely Generated ◽

Metabelian Groups ◽

Soluble Groups ◽

Group Extensions

This paper is devoted to the construction of faithful representations of the automorphism group and the holomorph of an extension of an abelian group by some other group, the representations here being homomorphisms into certain restricted parts of the automorphism groups of smallish abelian groups. We apply these to two very specific cases, namely to finitely generated metabelian groups and to certain soluble groups of finite rank. We describe the applications first.

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On the basis-conjugating automorphism groups of free groups and free metabelian groups

Mathematical Proceedings of the Cambridge Philosophical Society ◽

10.1017/s0305004114000619 ◽

2014 ◽

Vol 158 (1) ◽

pp. 83-109 ◽

Cited By ~ 1

Author(s):

TAKAO SATOH

Keyword(s):

Lie Algebra ◽

Automorphism Groups ◽

Free Groups ◽

Metabelian Groups ◽

Derivation Algebra ◽

Trace Maps

AbstractIn this paper we study the images of the Johnson homomorphisms of the basis-conjugating automorphism groups of free groups and free metabelian groups. In particular, we show that the Johnson image is contained in a certain proper Lie subalgebra $\mathfrak{p}$Mn of the derivation algebra of the Chen Lie algebra. Furthermore, we completely determine the Johnson images, and give the abelianisation of $\mathfrak{p}$Mn as a Lie algebra by using Morita's trace maps.

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