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Metacyclic p-groups and their conjugacy classes of subgroups

Published online by Cambridge University Press:  18 May 2009

Rolf Brandl  and
Libero Verardi
Rolf Brandl
Affiliation:
Mathematisches InstitutAm Hubland 12D-W-8700 WürzburgGermany
Libero Verardi
Affiliation:
Dipartimento Di MatematicaPiazza di Porta San Donato, 5 I-40127 BolognaItaly
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Let G be a group and let ℓ(G) be the set of all conjugacy classes [H] of subgroups H of G, where a partial order ≤ is defined by [H1] ≤ [H2] if and only if H1, is contained in some conjugate of H2.

A number of papers (see for example [1] and the references mentioned there) deal with the question of characterizing groups G by the poset ℓ(G). For example, in [1] it was shown that if ℓ(G) and ℓ(H) are order-isomorphic and G is a noncyclic p-group then |G| = |H|. Moreover, if G is abelian, then G = H, and if G is metacyclic then H is metacyclic.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 35 , Issue 3 , September 1993 , pp. 339 - 344
Copyright
Copyright © Glasgow Mathematical Journal Trust 1993

References

REFERENCES

1.Brandl, R., Posets of subgroups in p-groups. Comm. Algebra, 20 (10) (1992), 3043–3054.Google Scholar
2.Brandl, R., Caranti, A. and Scoppola, C. M., Metabelian thin p-groups, Quart. J. Math. (Oxford), (2) 43 (1992), 157–173.CrossRefGoogle Scholar
3.Heineken, H., Charakterisierung von Gruppen durch gewisse Untergruppenverbande, J. Reine Angew. Math. 220 (1965), 30–36.Google Scholar
4.Huppert, B., Endliche Gruppen I, Springer-Verlag, Berlin Heidelberg New York 1967.Google Scholar
5.King, B. W., Presentations of metacyclic groups. Bull. Austral. Math. Soc. 8 (1973), 103–131.Google Scholar