FINITE COVERS OF GROUPS BY COSETS OR SUBGROUPS
نویسندگان
چکیده
منابع مشابه
Finite 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 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 کاملOn 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 کاملAutomatic groups, subgroups and cosets
The history, definition and principal properties of automatic groups and their generalisations to subgroups and cosets are reviewed briefly, mainly from a computational perspective. A result about the asynchronous automaticity of an HNN extension is then proved and applied to an example that was proposed by Mark Sapir. AMS Classification 20F32; 20F05
متن کاملClassifying fuzzy normal subgroups of finite groups
In this paper a first step in classifying the fuzzy normalsubgroups of a finite group is made. Explicit formulas for thenumber of distinct fuzzy normal subgroups are obtained in theparticular cases of symmetric groups and dihedral groups.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: International Journal of Mathematics
سال: 2006
ISSN: 0129-167X,1793-6519
DOI: 10.1142/s0129167x06003813