منابع مشابه
Closest Multiplication Tables of Groups
Suppose that all groups of order n are defined on the same set G of cardinality n, and let the distance of two groups of order n be the number of pairs (a, b) ∈ G×G where the two group operations differ. Given a group G(◦) of order n, we find all groups of order n, up to isomorphism, that are closest to G(◦).
متن کاملOn the Mark and Markaracter Tables of Finite Groups
Let G be a finite group and C(G) be the family of representative conjugacy classes of subgroups of G. The matrix whose H,K-entry is the number of fixed points of the set G/K under the action of H is called the table of marks of G where H,K run through all elements in C(G). Shinsaku Fujita for the first time introduced the term “markaracter” to discuss marks for permutation representati...
متن کاملOn the Complexity of Some Problems on Groups Input as Multiplication Tables
The Cayley Group Membership problem (CGM) is to input a groupoid (binary algebra) G given as a multiplication table, a subset X of G, and an element t of G, and to determine whether t can be expressed as a product of elements of X. For general groupoids CGM is P-complete, and for associative algebras (semigroups) it is NL-complete. Here we investigate CGM for particular classes of groups. The p...
متن کاملCharacter Tables of Metacyclic Groups
We show that two metacyclic groups of the following types are isomorphic if they have the same character tables: (i) split metacyclic groups, (ii) the metacyclic p-groups and (iii) the metacyclic {p, q}-groups, where p, q are odd primes. 2010 Mathematics Subject Classification. Primary 20C15; Secondary 20D15, 20F16, 20F22.
متن کاملReconstruction of Group Multiplication Tables by Quadrangle Criterion
For n > 3, every n×n partial Cayley matrix with at most n−1 holes can be reconstructed by quadrangle criterion. Moreover, the holes can be filled in given order. Without additional assumptions, this is the best possible result. Reconstruction of other types of multiplication tables is discussed.
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2012
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2011.11.026