Hostname: page-component-848d4c4894-sjtt6 Total loading time: 0 Render date: 2024-07-07T04:22:56.708Z Has data issue: false hasContentIssue false
  • English
  • Français

Bigenetic properties of finitely generated hyper- (Abelian-by-finite) groups

Published online by Cambridge University Press:  09 April 2009

J. C. Lennox
J. C. Lennox
Affiliation:
University College Cardiff, CFI IXL Wales
Rights & Permissions [Opens in a new window]

Extract

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.

Let be a class and p a property of groups. We say that p is a bigenetic property of p-groups (or more simply, p is bigenetic in p-groups) if an p-group G has the property p whenever all two-generator subgroups of G have p.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 16 , Issue 3 , November 1973 , pp. 309 - 315
Copyright
Copyright © Australian Mathematical Society 1973

References

[1]Baer, R., ‘Representations of Groups as Quotient Groups II’, Trans. Amer. Math. Soc. 58 (1945), 348–389.Google Scholar
[2]Baer, R., ‘Nilgruppen’, Math. Z. 62 (1955), 402–437.CrossRefGoogle Scholar
[3]Carter, R. W., Fischer, B. and Hawkes, T., ‘Extreme Classes of Finite Soluble Groups’, J. Algebra 9 (1968), 285–313.CrossRefGoogle Scholar
[4]Gruenberg, K. W., ‘Two Theorems on Engel Groups’, Proc. Cambridge Philos. Soc. 49 (1953), 377–380.CrossRefGoogle Scholar
[5]Gruenberg, K. W., ‘The Engel Elements of a Soluble Groups’, Illinois J. Math. 3 (1959), 151–168.CrossRefGoogle Scholar
[6]Hall, P., ‘Finiteness Conditions for Soluble Groups’, Proc. London Math. Soc. (3) 4 (1954), 419–436.Google Scholar
[7]Hall, P., ‘Finite-by-nilpotent groups’, Proc. Cambridge Philos. Soc. 52 (1956), 611–616.CrossRefGoogle Scholar
[8]Hall, P., ‘On the Finiteness of Certain Soluble Groups’, Proc. London Math. Soc. (3) 9 (1959), 595–622.CrossRefGoogle Scholar
[9]Lennox, J. C. and Roseblade, J. E., ‘Centrality in Finitely Generated Soluble Groups’, J. Algebra 16 (1970), 399–435.CrossRefGoogle Scholar
[10]Lennox, J. C., ‘A Note on a Centrality Property in Finitely Generated Soluble Groups’, to appear in Proc. Cambridge Philos. Soc.Google Scholar
[11]Newman, M. F., ‘A Theorem of Golod-Šafarevič and an application in group theory’, unpublished.Google Scholar
[12]Robinson, D. J. S., ‘A Theorem on Finitely Generated Hyperabelian Groups’, Invent. Math. 10 (1970), 38–43.CrossRefGoogle Scholar
[13]Scott, W. R., Group Theory, (Prentice Hall, Englewood Cliffs, N.J. 1964).Google Scholar
[14]Segal, D., ‘Groups of Automorphisms of Infinite Soluble Groups’, Proc. London Math. Soc. (3) 26 (1973) 630–652.CrossRefGoogle Scholar
[15]Thompson, J. G., ‘Non solvable finite groups all of whose local subgroups are solvable’, Bull. Amer. Math. Soc. 74 (1968), 383–437.Google Scholar
[16]Wehrfritz, B. A. F., Infinite Linear Groups, (Queen Mary College Mathematics Notes, London, 1969.)Google Scholar
[17]Wehrfritz, B. A. F., ‘2-generator conditions in linear groups’, Arch. Math. (Basel) 22 (1971), 237–241.CrossRefGoogle Scholar
[18]Wehrfritz, B. A. F., ‘Supersoluble and Locally Supersoluble Linear Groups’, J. Algebra 17 (1971), 41–58.Google Scholar