منابع مشابه
On Covers of Abelian Groups by Cosets
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 ...
متن کاملExactm-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 · · ...
متن کاملNon-Abelian Sequenceable Groups Involving ?-Covers
A non-abelian finite group is called sequenceable if for some positive integer , is -generated ( ) and there exist integers such that every element of is a term of the -step generalized Fibonacci sequence , , , . A remarkable application of this definition may be find on the study of random covers in the cryptography. The 2-step generalized sequences for the dihedral groups studi...
متن کاملFinite Covers of Groups by Cosets or Subgroups
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=...
متن کاملnon-abelian sequenceable groups involving ?-covers
a non-abelian finite group is called sequenceable if for some positive integer , is -generated ( ) and there exist integers such that every element of is a term of the -step generalized fibonacci sequence , , , . a remarkable application of this definition may be find on the study of random covers in the cryptography. the 2-step generalized sequences for the dihedral groups studied for their pe...
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ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 2008
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa131-4-3