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Marek Karaś; Jakub Zygadło

doi:10.1016/j.jpaa.2011.04.003

On multidegrees of tame and wild automorphisms of C3

Journal of Pure and Applied Algebra ◽

10.1016/j.jpaa.2011.04.003 ◽

2011 ◽

Vol 215 (12) ◽

pp. 2843-2846 ◽

Cited By ~ 2

Author(s):

Marek Karaś ◽

Jakub Zygadło

Keyword(s):

Wild Automorphisms

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Defining relations for tame automorphism groups of polynomial rings and wild automorphisms of free associative algebras

Doklady Mathematics ◽

10.1134/s1064562406020219 ◽

2006 ◽

Vol 73 (2) ◽

pp. 229-233

Author(s):

U. U. Umirbaev

Keyword(s):

Automorphism Groups ◽

Polynomial Rings ◽

Associative Algebras ◽

Defining Relations ◽

Tame Automorphism ◽

Wild Automorphisms

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On Tame and Wild Automorphisms of Algebras

Journal of Mathematical Sciences ◽

10.1007/s10958-015-2342-4 ◽

2015 ◽

Vol 206 (6) ◽

pp. 660-667

Author(s):

C. K. Gupta ◽

V. M. Levchuk ◽

Yu. Yu. Ushakov

Keyword(s):

Wild Automorphisms

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ON THE AUTOMORPHISM GROUP OF A FREE METABELIAN LIE ALGEBRA

International Journal of Algebra and Computation ◽

10.1142/s0218196708004408 ◽

2008 ◽

Vol 18 (02) ◽

pp. 209-226 ◽

Cited By ~ 5

Author(s):

VITALY ROMAN'KOV

Keyword(s):

Automorphism Group ◽

Normal Subgroup ◽

Lie Algebra ◽

Free Subgroup ◽

Finite Set ◽

Free Metabelian Lie Algebra ◽

Inner Automorphisms ◽

Infinite Set ◽

Wild Automorphisms

Let K be a field of any characteristic. We prove that a free metabelian Lie algebra M3 of rank 3 over K admits wild automorphisms. Moreover, the subgroup I Aut M3 of all automorphisms identical modulo the derived subalgebra [Formula: see text] cannot be generated by any finite set of IA-automorphisms together with the sets of all inner and all tame IA-automorphisms. In the case if K is finite the group Aut M3 cannot be generated by any finite set of automorphisms together with the sets of all tame, all inner automorphisms and all one-row automorphisms. We present an infinite set of wild IA-automorphisms of M3 which generates a free subgroup F∞ modulo normal subgroup generated by all tame, all inner and all one-row automorphisms of M3.

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