Embedding Theorems for Groups

Neumann, Bernhard; Neumann, Hanna

doi:10.1112/jlms/s1-34.4.465

Cited by 87 publications

(90 citation statements)

References 2 publications

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“…First we see that the value / + 2 for the soluble length of the two-generator group obtained in [22] cannot be combined with 'verbality' of the embedding of Theorem 1. On the other hand we can construct an embedding preserving the rest of the properties listed above: every ordered soluble countable group G of soluble length I can be subnormally embedded into an ordered twogenerator soluble group of length 1 + 2, but not I + 1 in general (Theorem 2).…”

Section: Embeddings Of Soluble Groupsmentioning

confidence: 99%

“…Kovacs and B. Neumann have extended in [10] the result of [22] and have constructed embeddings of countable S/*-groups (of countable SN*-groups) into two-generator 5/*-groups (into two-generator SW-groups, respectively). It is very natural to ask whether one can 'add full order' to this embedding as well.…”

Section: Embeddings Of Soluble Groupsmentioning

confidence: 99%

“…Embeddings into a word subgroups B. Neumann and Hanna Neumann have constructed in [22] not simply an embedding into a two-generator group but also into the second derived group of the latter (see also [1]). Since two-generator groups also are countable we can, for arbitrary n, construct embeddings of this type into the nth member of the derived series of a suitable two-generator group.…”

Section: Embeddings Of Soluble Groupsmentioning

confidence: 99%

“…B. Neumann and Hanna Neumann have 380 Vahagn H. Mikaelian [2] proved that every soluble countable group of length / is embeddable into a soluble two-generator group of length at most 1 + 2 (but not / + 1 in general) [22].…”

Section: Embeddings Of Soluble Groupsmentioning

confidence: 99%

“…Since abelian (or nilpotent) groups are not in general embeddable into two-generator abelian (or nilpotent) groups [21,22], such embeddings of soluble groups are of special interest. B. Neumann and Hanna Neumann have 380 Vahagn H. Mikaelian [2] proved that every soluble countable group of length / is embeddable into a soluble two-generator group of length at most 1 + 2 (but not / + 1 in general) [22].…”

Section: Embeddings Of Soluble Groupsmentioning

confidence: 99%

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An Embedding Construction for Ordered Groups

Mikaelian¹

2003

J. Aust. Math. Soc.

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Generalizing and strengthening some well-known results of Higman, B. Neumann, Hanna Neumann and Dark on embeddings into two-generator groups, we introduce a construction of subnormal verbal embedding of an arbitrary (soluble, fully ordered or torsion free) ordered countable group into a twogenerator ordered group with these properties. Further, we establish subnormal verbal embedding of defect two of an arbitrary (soluble, fully ordered or torsion free) ordered group G into a group with these properties and of the same cardinality as G, and show in connection with a problem of Heineken that the defect of such an embedding cannot be made smaller, that is, such verbal embeddings of ordered groups cannot in general be normal.2000 Mathematics subject classification: primary 20E10, 20E15, 20E22, 20F14,06F15.

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Section: Embeddings Of Soluble Groupsmentioning

confidence: 99%

Section: Embeddings Of Soluble Groupsmentioning

confidence: 99%

Section: Embeddings Of Soluble Groupsmentioning

confidence: 99%

Section: Embeddings Of Soluble Groupsmentioning

confidence: 99%

Section: Embeddings Of Soluble Groupsmentioning

confidence: 99%

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An Embedding Construction for Ordered Groups

Mikaelian¹

2003

J. Aust. Math. Soc.

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On Embeddings of Countable Generalized Soluble Groups into Two-Generated Groups

Mikaelian¹

2002

Journal of Algebra

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to professor h. s. mikaelian, my father Strengthening a theorem of L. G. Kovács and B. H. Neumann on embeddings of countable SN * -and SI * -groups into two-generated SN * -and SI * -groups, we establish embeddability of fully ordered countable SN-, SN * -, SI-, and SI * -groups into appropriate fully ordered two-generated groups of the same type. Moreover, for an arbitrary non-trivial word set V ⊆ F ∞ the mentioned two-generated group can be chosen such that the verbal V -subgroup of the latter contains the order isomorphic copy of an initial countable group. These embeddings are subnormal but not, in general, normal.  2002 Elsevier Science (USA)

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Infinite Soluble Groups

Robinson

1996

A Course in the Theory of Groups

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Embedding Theorems for Groups

Cited by 87 publications

References 2 publications

An Embedding Construction for Ordered Groups

An Embedding Construction for Ordered Groups

On Embeddings of Countable Generalized Soluble Groups into Two-Generated Groups

Infinite Soluble Groups

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