On commutator subgroups

Acta Mathematica Hungarica -     

On the commutator of the Marcinkiewicz integral

boundedness is considered for the commutator of higher-dimensional Marcinkiewicz integral. Some conditions implying the and the boundedness for the commutator of the Marcinkiewicz integral are obtained.     

On the commutator length of a Dehn twist

We show that on a nonorientable surface of genus at least 7 any power of a Dehn twist is equal to a single commutator in the mapping class group and the same is true, under additional assumptions, for the twist subgroup, and also for the extended mapping class group of an orientable surface of genus at least 3.     

On conciseness of some commutator words

Archiv der Mathematik - We prove that a commutator of two non-commutator words is a concise word.     

On commutator subgroups of Artin groups

Doklady Mathematics -     

On the commutator subgroup of a nonconnected central group

In this paperG denotes a central topologicalT ₂-group—G/Z(G) compact, whereZ(G) is the center. There are some results concerning compactness of the commutator subgroupG; in general (G)^– is compact ([3]), but not necessarilyG ([7]). If in additionG is a Lie group or ifG is connected,G is compact ([6], [5]). The purpose of this paper is to show, that if the componentG ₀ of the identity is open,G must be compact, and to give an example of a compact group with (G/G ₀) compact, whileG is not compact.Dedicated to Prof. R. Inzinger on his 70th birthday     

On generalized commutators and nil commutator ideals

Archiv der Mathematik -     

On the centralizer and the commutator subgroup of an automorphism

Let φ be an automorphism of a group G. In this paper, we study the influence of its centralizer on its commutator subgroup when G is polycyclic or metabelian. For instance, when G is metabelian and φ fixed-point-free of prime order p, we prove that is nilpotent of class ≤ p. Also, when G is polycyclic and φ of order 2, we show that if is finite, then so are and .     

On a variant of commutator estimates in spectral theory

Completeness is proved for systems of two or three quantum particles. The proof is based on the following statement on operators in a Hilbert space. If an operator A is bounded with respect to a self-adjoint operator H and Re((H – )f, Af) Bf², then B is smooth with respect to H.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 163, pp. 29–36, 1987.     

On the centralizer and the commutator subgroup of an automorphism

Let φ be an automorphism of a group G. In this paper, we study the influence of its centralizer \({C_G(\varphi)}\) on its commutator subgroup \({[G,\varphi]}\) when G is polycyclic or metabelian. For instance, when G is metabelian and φ fixed-point-free of prime order p, we prove that \({[G,\varphi]}\) is nilpotent of class ≤ p. Also, when G is polycyclic and φ of order 2, we show that if \({C_G(\varphi)}\) is finite, then so are \({G/[G,\varphi]}\) and \({[G,\varphi]'}\) .     

On the commutator group of the group of interval exchange transformations

We study the group of interval exchange transformations and obtain several characterizations of its commutator group. In particular, it turns out that the commutator group is generated by elements of order 2.