Endomorphisms of two-generated metabelian groups that induce the identity modulo the derived subgroup

1991 ◽  
Vol 56 (3) ◽  
pp. 218-227 ◽  
Author(s):  
A. Caranti ◽  
C. M. Scoppola
Keyword(s):  
Metabelian Groups ◽  
Derived Subgroup ◽  
Identity Modulo

Automorphisms of partially commutative metabelian groups

2020 ◽  
Vol 59 (2) ◽  
pp. 239-259
Author(s):  
E. I. Timoshenko
Keyword(s):  
Metabelian Groups

Infinitely presented permutation stable groups and invariant random subgroups of metabelian groups

2021 ◽  
pp. 1-36
Author(s):  
ARIE LEVIT ◽  
ALEXANDER LUBOTZKY
Keyword(s):  
Ergodic Theorem ◽  
Abelian Groups ◽  
Wreath Products ◽  
Finitely Generated ◽  
Metabelian Groups ◽  
Amenable Groups ◽  
Pointwise Ergodic Theorem ◽  
Lamplighter Group ◽  
Invariant Random Subgroups

Abstract We prove that all invariant random subgroups of the lamplighter group L are co-sofic. It follows that L is permutation stable, providing an example of an infinitely presented such group. Our proof applies more generally to all permutational wreath products of finitely generated abelian groups. We rely on the pointwise ergodic theorem for amenable groups.

scholarly journals Another Law for the 3-Metabelian Groups

1966 ◽  
Vol 6 (4) ◽  
pp. 512-512
Author(s):  
I. D. Macdonald
Keyword(s):  
Mathematical Society ◽  
Metabelian Groups ◽  
Commutator Identity ◽  
Australian Mathematical Society ◽  
Correct Form ◽  
Image Position

Journal of the Australian Mathematical Society 4 (1964), 452–453The second paragraph should be deleted. The alleged commutator identity (3) is false and is certainly not due to Philip Hall. The correct form isas Dr. N. D. Gupta of Canberra has pointed out to me. According to Professor B. H. Neumann, this identity appeared in his (Professor Neumann's) thesis.Nevertheless the theorem is valid and the proof given is correct.

Metabelian groups with a single defining relation and the Magnus embedding

1995 ◽  
Vol 57 (4) ◽  
pp. 414-420
Author(s):  
E. I. Timoshenko
Keyword(s):  
Metabelian Groups ◽  
Defining Relation ◽  
Magnus Embedding

scholarly journals A combinatorial approach to the character theory of split metabelian groups

1989 ◽  
Vol 50 (1) ◽  
pp. 100-109
Author(s):  
Andrew J Woldar
Keyword(s):  
Character Theory ◽  
Combinatorial Approach ◽  
Metabelian Groups

scholarly journals Duality and the existence of weakly completely continuous elements in aB*-algebra

1972 ◽  
Vol 13 (1) ◽  
pp. 56-60 ◽  
Author(s):  
B. J. Tomiuk
Keyword(s):  
Hilbert Space ◽  
Left Ideal ◽  
Linear Operators ◽  
Completely Continuous ◽  
Identity Modulo

Ogasawara and Yoshinaga [9] have shown that aB*-algebra is weakly completely continuous (w.c.c.) if and only if it is*-isomorphic to theB*(∞)-sum of algebrasLC(HX), where eachLC(HX)is the algebra of all compact linear operators on the Hilbert spaceHx.As Kaplansky [5] has shown that aB*-algebra isB*-isomorphic to theB*(∞)-sum of algebrasLC(HX)if and only if it is dual, it follows that a5*-algebraAis w.c.c. if and only if it is dual. We have observed that, if only certain key elements of aB*-algebraAare w.c.c, thenAis already dual. This observation constitutes our main theorem which goes as follows.A B*-algebraAis dual if and only if for every maximal modular left idealMthere exists aright identity modulo M that isw.c.c.

Right and left engel elements in metabelian groups

1981 ◽  
Vol 9 (12) ◽  
pp. 1295-1306 ◽  
Author(s):  
Luise-Charlotte Kappe
Keyword(s):  
Metabelian Groups ◽  
Engel Elements

scholarly journals Homological finiteness conditions for a class of metabelian groups

2017 ◽  
Vol 50 (1) ◽  
pp. 17-25
Author(s):  
Peter H. Kropholler ◽  
Joseph P. Mullaney
Keyword(s):  
Finiteness Conditions ◽  
Metabelian Groups

PROJECTIVE METABELIAN GROUPS AND LIE ALGEBRAS

1978 ◽  
Vol 12 (2) ◽  
pp. 213-223 ◽  
Author(s):  
V A Artamonov
Keyword(s):  
Lie Algebras ◽  
Metabelian Groups

Nilpotent approximations of metabelian groups

1981 ◽  
Vol 20 (6) ◽  
pp. 413-423 ◽  
Author(s):  
D. I. Zaitsev
Keyword(s):  
Metabelian Groups
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