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Maximal subgroups and the Jordan-Hölder Theorem

Part of: Representation theory of groups

Published online by Cambridge University Press:  09 April 2009

Julio Lafuente
Julio Lafuente
Affiliation:
Departamento de Matemáticas, Universidad de Zaragoza, 50 009 Zaragoza, Spain
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Abstract

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In this note we present a general Jordan-Hölder type theorem for modular lattices and apply it to obtain various (old and new) versions of the Jordan-Hölder Theorem for finite groups.

MSC classification

Secondary: 20D30: Series and lattices of subgroups
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 46 , Issue 3 , June 1989 , pp. 356 - 364
Copyright
Copyright © Australian Mathematical Society 1989

References

[1]Baer, R., ‘Classes of finite groups and their properties’, Illinois J. Math. 1 (1987), 115–187.Google Scholar
[2]Baer, R. and Förster, P., Einbettungsrelationen und Formationen endlicher Gruppen, to appear.Google Scholar
[3]Barnes, D. W., ‘On complemented chief factors of finite soluble groups’, Bull. Austral. Math. Soc. 7 (1972), 101–104.CrossRefGoogle Scholar
[4]Carter, R. W., Fischer, B. and Hawkes, T. O., ‘Extreme classses of finite soluble groups’, J. Algebra 9 (1968), 285–313.CrossRefGoogle Scholar
[5]Förster, P., ‘Projektive Klassen endlicher Gruppen. I’, Math. Z. 186 (1984), 149–178.CrossRefGoogle Scholar
[6]Förster, P., ‘A note on primitive groups with small maximal subgroups’, Publ. Sec. Mat. Univ. Autonoma Barcelona 28 (1984), 19–28.Google Scholar
[7]Förster, P., ‘Chief factors, crowns, and the generalized Jordan-Hölder Theorem’, Comm. Algebra, to appear.Google Scholar
[8]Förster, P., ‘On primitive groups with regular normal subgroups’, ANU-MSRC Research Report 39–1985, Canberra.Google Scholar
[9]Grätzer, G., General lattice theory (Birkhäuser-Verlag, Basel, 1978).CrossRefGoogle Scholar
[10]Isbell, J. R., ‘Zassenhaus' Theorem supersedes the Jordan-Hölder Theorem’, Adv. in Math. 31 (1979), 101–103.CrossRefGoogle Scholar
[11]Kovács, L. G. and Newman, M. F., ‘On the Jordan-Hölder Theorem’, ANU-MSRC Research Report 11, 1987, Canberra.Google Scholar
[12]Lafuente, J., ‘Homomorphs and formations of given derived class’, Math. Proc. Cambridge Philos. Soc. 84 (1978), 437–441.CrossRefGoogle Scholar
[13]Lafuente, J., ‘Nonabelian crowns and Schunck classes of finite groups’, Arch. Math. 42 (1984), 32–39.CrossRefGoogle Scholar
[14]Lafuente, J., ‘Grupos primitivos con subgrupos maximales pequeños’, Publ. Sec. Mat. Univ. Autonoma Barcelona 29 (1985), 154–161.Google Scholar
[15]Neumann, H., Varieties of groups (Springer-Verlag, Berlin, Heidelberg, New York, 1967).CrossRefGoogle Scholar