Hostname: page-component-5c6d5d7d68-lvtdw Total loading time: 0 Render date: 2024-08-16T06:34:01.175Z Has data issue: false hasContentIssue false
  • English
  • Français

Supersolvable M*-groups

Published online by Cambridge University Press:  18 May 2009

Coy L. May
Coy L. May
Affiliation:
Department of Mathematics, Towson State University, Baltimore, Maryland 21204, U.S.A.
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.

A compact bordered Klein surface of genus g ≥ 2 has maximal symmetry [4] if its automorphism group is of order 12(g − 1), the largest possible. An M*-group [8] acts on a bordered surface with maximal symmetry. The first important result about these groups was that they must have a certain partial presentation [8, p. 5]. However, research has tended to focus more on the surfaces with maximal symmetry than on the M*-groups, and results about these groups typically deal with existence.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 30 , Issue 1 , January 1988 , pp. 31 - 40
Copyright
Copyright © Glasgow Mathematical Journal Trust 1988

References

1.Blackburn, N., On a special class of p-groups, Ada Math. 100 (1958), 45–92.Google Scholar
2.Gordejuela, J. J. Etayo, Klein surfaces with maximal symmetry and their groups of automorphisms, Math. Ann. 268 (1984), 533–538.CrossRefGoogle Scholar
3.Gorenstein, D., Finite groups, (Harper and Row, 1968).Google Scholar
4.Greenleaf, N. and May, C. L., Bordered Klein surfaces with maximal symmetry, Trans. Amer. Math. Soc. 274 (1982), 265–283.CrossRefGoogle Scholar
5.Hall, M., The theory of groups (Macmillan, 1959).Google Scholar
6.Hall, P., A contribution to the theory of groups of prime-power order, Proc. London Math. Soc. (2) 36 (1933), 29–95.Google Scholar
7.Huppert, B., Normalteiler und maximale Untergruppen endlicher Gruppen, Math. Z. 60 (1954), 409–434.CrossRefGoogle Scholar
8.May, C. L., Large automorphism groups of compact Klein surfaces with boundary, Glasgow Math. J. 18 (1977), 1–10.Google Scholar
9.May, C. L., Maximal symmetry and fully wound coverings, Proc. Amer. Math. Soc. 79 (1980), 23–31.CrossRefGoogle Scholar
10.May, C. L., The species of bordered Klein surfaces with maximal symmetry of low genus, Pacific J. Math. 111 (1984), 371–394.CrossRefGoogle Scholar
11.May, C. L., A family of M*-groups, Canad. J. Math. 38 (1986), 1094–1109.Google Scholar
12.Rose, J. S., A course on group theory, (Cambridge University Press, 1978).Google Scholar