Hostname: page-component-78c5997874-fbnjt Total loading time: 0 Render date: 2024-11-03T01:41:15.727Z Has data issue: false hasContentIssue false
  • English
  • Français

On prime-power groups with two generators

Published online by Cambridge University Press:  24 October 2008

N. Blackburn
N. Blackburn
Affiliation:
Trinity CollegeCambridge
Get access Rights & Permissions [Opens in a new window]

Extract

Let G denote a group of order a power of the prime p, and let G′ be the derived group of G. The lower central series of G will be written

For any subgroup H of G we denote by P(H) the subgroup of H generated by all elements xp as x runs through H, and by Φ(H) the Frattini subgroup of H. We write (H:Φ(H)) = pd(H); thus d(H) is the minimal number of generators of H.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 54 , Issue 3 , July 1958 , pp. 327 - 337
Copyright
Copyright © Cambridge Philosophical Society 1958

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Blackburn, N.On prime-power groups in which the derived group has two generators. Proc. Camb. Phil. Soc. 53 (1957), 19–27.CrossRefGoogle Scholar
(2)Blackburn, N.Über das Produkt von zwei zyklischen 2-Gruppen. Math. Z. 68 (1958), 422–7.CrossRefGoogle Scholar
(3)Hall, P.A contribution to the theory of groups of prime-power order. Proc. Land. Math. Soc. (2), 36 (1933), 29–95.Google Scholar
(4)Huppert, B.Über das Produkt von paarweise vertauschbaren zyklischen Gruppen. Math. Z. 58 (1953), 243–64.CrossRefGoogle Scholar
(5)Itô, N.Über das Produkt von zwei zyklischen 2-Gruppen. Publ. Math., Debrecen, 4 (1956), 517–20.Google Scholar
(6)Itô, N. and ôhara, A.Sur les groups factorisables par deux 2-groupes cycliques. Proc. Japan Acad. 32 (1956), 736–43.Google Scholar
(7)Meier-Wunderli, H.Über endliche p-Gruppen, deren Elemente der Gleichung xv = 1 genügen. Comment. math. Helvet. 24 (1950), 18–45.CrossRefGoogle Scholar
(8)Schreier, O.Die Untergruppen der freien Gruppen. Abh. math. Sem. Hamburg Univ. 5 (1927), 161–83.CrossRefGoogle Scholar
(9)Zassenhaus, H.Lehrbuch der Gruppentheorie (Leipzig-Berlin, 1937).Google Scholar