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Covering groups with subgroups

Published online by Cambridge University Press:  17 April 2009

R.A. Bryce ,
V. Fedri  and
L. Serena
R.A. Bryce
Affiliation:
School of Mathematical Sciences, The Australian National University, Canberra ACT 0200, Australia
V. Fedri
Affiliation:
School of Mathematical Sciences, The Australian National University, Canberra ACT 0200, Australia
L. Serena
Affiliation:
Dipartimento di Matematica, viale Morgagni 67/A, 50134 Firenze, Italia
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A group is covered by a collection of subgroups if it is the union of the collection. The intersection of an irredundant cover of n subgroups is known to have index bounded by a function of n, though in general the precise bound is not known. Here we confirm a claim of Tompkinson that the correct bound is 16 when n is 5. The proof depends on determining all the ‘minimal’ groups with an irredundant cover of five maximal subgroups.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 55 , Issue 3 , June 1997 , pp. 469 - 476
Copyright
Copyright © Australian Mathematical Society 1997

References

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