A class of SQ-Universal groups

Levin, Frank; Rosenberger, Gerhard; Cheng, Kai N.; Leong, Yu K.

doi:10.1515/9783110848397-031

Cited by 19 publications

(6 citation statements)

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“…We now deal with the four exceptional cases excluded in (i). These groups have been investigated in [15] (see also [3,5]) and the groups F(2,3;2), F(3,3;2) are finite of orders 24, 288 respectively while the groups F(2,3; 3), F(2,4; 2) are infinite and solvable. We see immediately that the second group cannot have a faithful discrete representation in PSL(2,C).…”

Section: Notation Throughout We Will Use R(x) To Denote the Trace Omentioning

confidence: 99%

On discrete generalised triangle groups

Hagelberg

MacLachlan

Rosenberger

1995

Proceedings of the Edinburgh Mathematical Society

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A generalised triangle group has a presentation of the form where R is a cyclically reduced word involving both x and y. When R=xy, these classical triangle groups have representations as discrete groups of isometries of S 2 , R 2 , H 2 depending on In this paper, for other words R, faithful discrete representations of these groups in Isom + H 3 = PSL(2,C) are considered with particular emphasis on the case /? = [x, y] and also on the relationship between the Euler characteristic x and finite covolume representations.1991 Mathematics subject classification: 20H15.

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Section: Notation Throughout We Will Use R(x) To Denote the Trace Omentioning

confidence: 99%

On discrete generalised triangle groups

Hagelberg

MacLachlan

Rosenberger

1995

Proceedings of the Edinburgh Mathematical Society

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“…The theorem, called in the book of Robinson [16] "probably the most famous of all embedding theorems", was a stimulus for further research on embeddings into 2-generated groups and related problems. See the papers of Ol'shanskii [14] [15], Galvin [2], B. Neumenn [11], Wilson and Zalesskii [17], Levin and Rosenberger [9], and literature cited there.…”

Section: Introduction and The Main Resultsmentioning

confidence: 99%

Subnormal Embedding Theorems for Groups

Mikaelian

2000

Journal of the London Mathematical Society

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Abstract. 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.

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“…For other results in this direction we refer to the papers of Ol'shanskii [25,26], B. Neumann [21], Levin and Rosenberger [13], Hall [4], Wilson and Zalesskii [28] and to literature cited there.…”

Section: Embeddings Of Soluble Groupsmentioning

confidence: 99%

“…D of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/S1446788700003372 [13] An embedding construction 391…”

Section: Some Related Problemsmentioning

confidence: 99%

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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A class of SQ-Universal groups

Cited by 19 publications

References 0 publications

On discrete generalised triangle groups

On discrete generalised triangle groups

Subnormal Embedding Theorems for Groups

An Embedding Construction for Ordered Groups

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