Subnormal Embedding Theorems for Groups
نویسندگان
چکیده
In this paper we establish some subnormal embeddings of groups into groups with additional properties; in particular embeddings of countable groups into 2-generated groups with some extra properties. The results obtained are generalizations of theorems of P. Hall, R. Dark, B. Neumann, Hanna Neumann, G. Higman on embeddings of that type. Considering subnormal embeddings of finite groups into finite groups with additional properties we bring some illustration to a result of H. Heineken and J. Lennox.
منابع مشابه
ar X iv : 1 50 2 . 06 47 2 v 1 [ m at h . R A ] 8 N ov 2 01 4 Gröbner - Shirshov bases and PBW theorems ∗
We review some applications of Gröbner-Shirshov bases, including PBW theorems, linear bases of free universal algebras, normal forms for groups and semigroups, extensions of groups and algebras, embedding of algebras.
متن کاملLifting strong commutants of unbounded subnormal operators
Various theorems on lifting strong commutants of unbounded sub-normal (as well as formally subnormal) operators are proved. It is shown that the strong symmetric commutant of a closed symmetric operator S lifts to the strong commutant of some tight selfadjoint extension of S. Strong symmetric commutants of orthogonal sums of subnormal operators are investigated. Examples of (unbounded) irreduci...
متن کاملFinite subnormal coverings of certain solvable groups
A group is said to have a finite covering by subgroups if it is the set theoretic union of finitely many subgroups. A theorem of B. H. Neumann [11] characterizes groups with finite coverings by proper subgroups as precisely those groups with finite non-cyclic homomorphic images. R. Baer (see [13, Theorem 4.16]) proved that a group has a finite covering by abelian subgroups if and only if it is ...
متن کاملSmall cancellations over relatively hyperbolic groups and embedding theorems
In this paper we generalize the small cancellation theory over hyperbolic groups developed by Olshanskii to the case of relatively hyperbolic groups. This allows us to construct infinite finitely generated groups with exactly n conjugacy classes for every n ≥ 2. In particular, we give the affirmative answer to the well–known question of the existence of a finitely generated group G other than Z...
متن کاملC∗-algebras Generated by a Subnormal Operator
Using the functional calculus for a normal operator, we provide a result for generalized Toeplitz operators, analogous to the theorem of Axler and Shields on harmonic extensions of the disc algebra. Besides that result, we prove that if T is an injective subnormal weighted shift, then any two nontrivial subspaces invariant under T cannot be orthogonal to each other. Then we show that the C∗-alg...
متن کامل