منابع مشابه
The CI Problem for Infinite Groups
A finite group G is a DCI-group if, whenever S and S′ are subsets of G with the Cayley graphs Cay(G,S) and Cay(G,S′) isomorphic, there exists an automorphism φ of G with φ(S) = S′. It is a CI-group if this condition holds under the restricted assumption that S = S−1. We extend these definitions to infinite groups, and make two closely-related definitions: an infinite group is a strongly (D)CIf ...
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برد عددی ماتریس مربعی a را با w(a) نشان داده و به این صورت تعریف می کنیم w(a)={x8ax:x ?s1} ، که در آن s1 گوی واحد است. در سال 2009، راسل کاردن مساله برد عددی معکوس را به این صورت مطرح کرده است : برای نقطه z?w(a)، بردار x?s1 را به گونه ای می یابیم که z=x*ax، در این پایان نامه ، الگوریتمی برای حل مساله برد عددی معکوس ارانه می دهیم.
15 صفحه اولQuotients of CI-Groups are CI-Groups
We show that a quotient group of a CI-group with respect to (di)graphs is a CI-group with respect to (di)graphs. In [1,2], Babai and Frankl provided strong constraints on which finite groups could be CI-groups with respect to graphs. As a tool in this program, they proved [1, Lemma 3.5] that a quotient group G/N of a CI-group G with respect to graphs is a CI-group with respect to graphs provide...
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Let G be an infinite abelian group with |2G| = |G|. We show that if G is not the direct sum of a group of exponent 3 and the group of order 2, then G possesses a perfect additive basis; that is, there is a subset S ⊆ G such that every element of G is uniquely representable as a sum of two elements of S. Moreover, if G is the direct sum of a group of exponent 3 and the group of order 2, then it ...
متن کاملA Combinatorial Problem in Infinite Groups
Let w be a word in the free group of rank n ∈ N and let V(w) be the variety of groups defined by the law w = 1. Define V(w∗) to be the class of all groups G in which for any infinite subsets X1, . . . , Xn there exist xi ∈ Xi, 1 ≤ i ≤ n, such that w(x1, . . . , xn) = 1. Clearly, V(w) ∪ F ⊆ V(w ∗); F being the class of finite groups. In this paper, we investigate some words w and some certain cl...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2016
ISSN: 1077-8926
DOI: 10.37236/5056