منابع مشابه
Exactm-covers of Groups by Cosets
Let G be a group covered by its left cosets a1G1, · · · , akGk exactly m times. It is known that [G : ⋂k i=1 Gi] 6 k!. When all the Gi are subnormal in G and ⋂k i=1 Gi = H, we are able to determine the least value of k in terms of m,G,H. For any i = 1, · · · , k, providing G/(Gi)G is solvable we show that k > m + f([G : Gi]) and hence [G : Gi] 6 2k−m, where f(n) = ∑r s=1 αs(ps − 1) if p1 1 · · ...
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Let G be any abelian group and {asGs}ks=1 be a finite system of cosets of subgroups G1, . . . , Gk. We show that if {asGs} k s=1 covers all the elements of G at least m times with the coset atGt irredundant then [G : Gt] 6 2 and furthermore k > m + f([G : Gt]), where f( ∏ r i=1 p αi i ) = ∑ r i=1 αi(pi − 1) if p1, . . . , pr are distinct primes and α1, . . . , αr are nonnegative integers. This ...
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Abstract. This paper deals with combinatorial aspects of finite covers of groups by cosets or subgroups. Let a1G1, . . . , akGk be left cosets in a group G such that {aiGi} k i=1 covers each element of G at least m times but none of its proper subsystems does. We show that if G is cyclic, or G is finite and G1, . . . , Gk are normal Hall subgroups of G, then the inequality k > m + f([G : ⋂ k i=...
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ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 2001
ISSN: 0195-6698
DOI: 10.1006/eujc.2000.0466