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An Amalgamation Theorem For Soluble Groups

Published online by Cambridge University Press:  20 November 2018

Felix Leinen*
Affiliation:
Fachbereich 17 - Mathematik Johannes-Gutenberg-Universitât Saarstr. 21 6500 Mainz West-Germany
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Abstract

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A theorem of G. Higman about the embeddability of amalgams within the class of all finite ρ-groups is generalized to classes of soluble groups. We also give best possible bounds for the solubility lengths of the constructed completions. And, as an application, the super-soluble amalgamation bases in the class of all finite soluble π-groups are determined.

Keywords

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 01

References

1. Allenby, R.B.J.T., Generalized regular products of groups, Ph.D. thesis, Wales, 1966 (unpublished).Google Scholar
2. Gregorac, R.J, On permutational products of groups, J. Austral. Math. Soc, 10 (1969), pp. 111 — 135.Google Scholar
3. Hall, P., Some constructions for locally finite groups, J. London Math. Soc., 34 (1959), pp. 305 — 319.Google Scholar
4. Hickin, K., An amalgamation theorem for group extensions, Arch. Math., 45 (1985), pp. 485—491.Google Scholar
5. Higman, G., Amalgams of p-groups, J. Algebra, 1 (1964), pp. 301305.Google Scholar
6. Leinen, F., Existentially closed L-groups, Rend. Sem. Mat. Univ. Padova, 75 (1986), pp. 191226.Google Scholar
7. Neumann, B.H and Wiegold, J., On certain embeddability criteria for group amalgams, Publ. Math. Debrecen, 9 (1962), pp. 5764.Google Scholar
8. Neumann, P.M, On the structure of standard wreath products of groups. Math. Z., 84 (1964), pp. 343373.Google Scholar
9. Wiegold, J., Soluble embeddings of group amalgams, Publ. Math. Debrecen, 12 (1965), pp. 227230.Google Scholar