Groups covered by finitely many cosets or subgroups

Tomkinson, M. J.

doi:10.1080/00927878708823445

Cited by 51 publications

(26 citation statements)

References 4 publications

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“…Covers of groups have been studied by many authors. For example Neumann [5] shows that the intersection of the members of an irredundant cover with n members has index bounded by a function of n. Tomkinson [8] improved this bound. Minimal covers seem to have been introduced by Cohn [1]; and Tomkinson [9] showed that, for a finite soluble group G, o(G) is p a + 1 where p a is the size of the smallest chief factor of G with multiple complements.…”

Section: Introductionmentioning

confidence: 99%

Subgroup coverings of some linear groups

Bryce

Fedri²,

Serena³

1999

Bull. Austral. Math. Soc.

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Dedicated to Bernhard Neumann on his 90th birthday.A cover for a group is a collection of proper subgroups whose union is the whole group. A cover is minimal if no other cover contains fewer members. We term minimised a minimal cover with the property that substituting for a member of the cover by a proper subgroup of that member produces a collection which is no longer a cover. We here describe the minimised covers for the groups GL 2 (q), SL 2 (g), PSL 2 (

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Section: Introductionmentioning

confidence: 99%

Subgroup coverings of some linear groups

Bryce

Fedri²,

Serena³

1999

Bull. Austral. Math. Soc.

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“…(7) G ∼ = (C 2 ) 6 Sym 3 and |D| = 6. Neumann [7] proved that if G has an irredundant n-cover then the index of the intersection of the cover in G is bounded by a function of n. Tomkinson [10] improved that bound and gave estimates for f (n), the largest index |G : D| over all groups G having an irredundant n-cover with intersection D. He suggested that the lower bound In [8,6,2], the value of f (n) was obtained for n = 3, 4, 5, namely f (3) = g(3), f (4) = g(4) and f (5) = g(5), respectively. Also Abdollahi et al [1] have shown that f (6) = g (6).…”

Section: Introduction and Resultsmentioning

confidence: 99%

On groups with an irredundant 7-cover

Abdollahi¹,

Amiri²

2007

Journal of Pure and Applied Algebra

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A cover for a group is a collection of proper subgroups whose union is the whole group. A cover is irredundant if no proper sub-collection is also a cover and is called maximal if all its members are maximal subgroups. For an integer n > 2, a cover with n members is called an n-cover. In this paper we determine groups with a maximal irredundant 7-cover with core-free intersection. The intersection of an irredundant n-cover is known to have index bounded by a function of n, though in general the precise bound is not known. Here we prove that the exact bound is 81 when n is 7.

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“…Further problems of a similar nature, with slightly different aspects, have been studied by many people (see [16,19,20]).…”

Section: Theorem 13 ( See [2]mentioning

confidence: 99%

Identification of C_8-groups by central core

Ataei¹

2017

ija

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Let G denotes a semisimple C 8-group and {M i |1 ≤ i ≤ 8} be a maximal irredundant 8-cover for G, with core-free intersection D = 8 i=1 M i. Also for each i, 1 ≤ i ≤ 8 we assume that |G : M i | = α i such that α 1 ≤ α 2 ≤ α 3 ≤ α 4 ≤ α 5 ≤ α 6 ≤ α 7 ≤ α 8. Let G be a C n-group, we say that G is a core i2-group if (M i) G ∩ (M j) G = 1 for 3 ≤ i < j ≤ 8. Also let G be a C n-group and core i2-group, then we say that N := (M 1) G ∩ (M 2) G central core of G. In this paper we show that if G be a semisimple C 8-group and α l ≤ 4 then G is core i-2 group. Also we give some results for central core of G.

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Groups covered by finitely many cosets or subgroups

Cited by 51 publications

References 4 publications

Subgroup coverings of some linear groups

Subgroup coverings of some linear groups

On groups with an irredundant 7-cover

Identification of C_8-groups by central core

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