Hostname: page-component-586b7cd67f-rdxmf Total loading time: 0 Render date: 2024-12-01T00:06:32.587Z Has data issue: false hasContentIssue false
  • English
  • Français

A new embedding scheme for groups and some applications

Part of: Special aspects of infinite or finite groups

Published online by Cambridge University Press:  09 April 2009

Viatcheslav N. Obraztsov
Viatcheslav N. Obraztsov
Affiliation:
Facutly of Mathematics and Physics Kostroma Pedagogical UniversityFirst of May 14, Kostroma 156601, Russia
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper a scheme of an ‘economical’ embedding of an arbitrary set of groups without involutions in an infinite group with a proper simple normal subgroup is presented. This scheme is then applied to construction of groups with new properties.

MSC classification

Secondary: 20F05: Generators, relations, and presentations 20F06: Cancellation theory; application of van Kampen diagrams
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 61 , Issue 2 , October 1996 , pp. 267 - 288
Copyright
Copyright © Australian Mathematical Society 1996

References

[1]Ivanov, S. G., ‘Standard and dually standard elements of the lattice of subgroups of a group’, Algebra i Logika 8 (1969), 440–446Google Scholar
(translation: Algebra and Logic 8 (1969) 253–256).CrossRefGoogle Scholar
[2]Ivanov, S. V., ‘Two remarks on groups of finite period’, in: 19th All-Union Algebraic Conf., Res. Comm. Part 2, L'vov (1987), 105.Google Scholar
[3]Kazarin, L. S. and Kurdachenko, L. A., ‘Conditions for finiteness and factorization in infinite groups’, Uspekhi Mat. Nauk 47 (1992), 75–114; (English translation:Google Scholar
Russian Math. Surveys 47 1992, 81–126).CrossRefGoogle Scholar
[4]Kourovka Notebook: unsolved problems of group theory, 12th edition (Inst. Math. Siberian Dep. Russian Acad. Sci., Novosibirsk, 1992).Google Scholar
[5]Matumoto, T., ‘Any group is represented by outer automorphism group’, Hiroshima Math. J. 19 (1989), 209–219.CrossRefGoogle Scholar
[6]Napolitani, F., ‘Sui gruppi risolubili complementati’, Rend. Sem. Mat. Univ. Padova 38 (1967), 118–120.Google Scholar
[7]Obraztsov, V. N., ‘An embedding theorem for groups and its corollaries’, Mat. Sb. 180 (1989), 529–541Google Scholar
(English translation: Math. USSR-Sb. 66 1990, 541–553).CrossRefGoogle Scholar
[8]Obraztsov, V. N., ‘Embedding schemes for groups and some applications’, deposited VINITI 8 02 1990, no. 724–B90.Google Scholar
[9]Obraztsov, V. N., ‘On infinite complete groups’, Comm. Algebra 22 (1994), 5875–5887.CrossRefGoogle Scholar
[10]Ol'shanskii, A. Yu., Geometry of defining relations in groups (Nauka, Moscow, 1989); English translation: (North Holland, Amsterdam, 1991).Google Scholar
[11]Stonehewer, S. and Zacher, G., ‘Dual-standard subgroups in nonperiodic locally soluble groups’, Atti. Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (9) Mat. Appl. 1 (1990), 101–104.Google Scholar
[12]Zappa, G., ‘Sulla condizione perche un emitropismo inferiore tipico tra due gruppi sia un omotropismo’, Giorn. Mat. Battaglini(4) 80 (1951), 80–101.Google Scholar