Book contents
- Frontmatter
- Contents
- Contents of Volume II
- Introduction
- Radical rings and products of groups
- Homogeneous integral table algebras of degrees two, three and four with a faithful element
- A polynomial-time theory of black box groups I
- Totally and mutually permutable products of finite groups
- Ends and algebraic directions of pseudogroups
- On locally nilpotent groups with the minimal condition on centralizers
- Infinite groups in projective and symplectic geometry
- Non-positive curvature in group theory
- Group-theoretic applications of non-commutative toric geometry
- Theorems of Kegel-Wielandt type
- Singly generated radicals associated with varieties of groups
- The word problem in groups of cohomological dimension
- Polycyclic-by-finite groups: from affine to polynomial structures
- On groups with rank restrictions on subgroups
- On distances of multiplication tables of groups
- The Dade conjecture for the McLaughlin group
- Automorphism groups of certain non-quasiprimitive almost simple graphs
- Subgroups of the upper-triangular matrix group with maximal derived length and a minimal number of generators
- On p-pronormal subgroups of finite p-soluble groups
- On the system of defining relations and the Schur multiplier of periodic groups generated by finite automata
- On the dimension of groups acting on buildings
- Dade's conjecture for the simple Higman-Sims group
- On the F*-theorem
- Covering numbers for groups
- Characterizing subnormally closed formations
- Symmetric words in a free nilpotent group of class 5
- A non-residually finite square of finite groups
On distances of multiplication tables of groups
Published online by Cambridge University Press: 05 August 2013
- Frontmatter
- Contents
- Contents of Volume II
- Introduction
- Radical rings and products of groups
- Homogeneous integral table algebras of degrees two, three and four with a faithful element
- A polynomial-time theory of black box groups I
- Totally and mutually permutable products of finite groups
- Ends and algebraic directions of pseudogroups
- On locally nilpotent groups with the minimal condition on centralizers
- Infinite groups in projective and symplectic geometry
- Non-positive curvature in group theory
- Group-theoretic applications of non-commutative toric geometry
- Theorems of Kegel-Wielandt type
- Singly generated radicals associated with varieties of groups
- The word problem in groups of cohomological dimension
- Polycyclic-by-finite groups: from affine to polynomial structures
- On groups with rank restrictions on subgroups
- On distances of multiplication tables of groups
- The Dade conjecture for the McLaughlin group
- Automorphism groups of certain non-quasiprimitive almost simple graphs
- Subgroups of the upper-triangular matrix group with maximal derived length and a minimal number of generators
- On p-pronormal subgroups of finite p-soluble groups
- On the system of defining relations and the Schur multiplier of periodic groups generated by finite automata
- On the dimension of groups acting on buildings
- Dade's conjecture for the simple Higman-Sims group
- On the F*-theorem
- Covering numbers for groups
- Characterizing subnormally closed formations
- Symmetric words in a free nilpotent group of class 5
- A non-residually finite square of finite groups
Summary
Abstract
If G(*) and G(∘) are two different groups on the same set, then their distance is defined as the number of pairs (a, b) ∈ G × G with a * b ≠ a ∘ b. Questions about minimal possible distances lead to different problems as isomorphic groups are or are not admitted. The paper presents many facts known about these problems and establishes the minimal distance of an element ary-ab elian 2-group from non-isomorphic groups of the same order.
Introduction
The purpose of this paper is to report on facts known about (Hamming) distances of finite groups and to prove some new results in this area.
If G(∘) and G(*) are two groups on G, then their distance dist(G(∘), G(*)) is defined to be the number of pairs (a, b) ∈ G × G with a ∘ b ≠ a * b. For a fixed group G(∘) define δ(G(∘)) to be the minimum of dist(G(∘), G(*)), where G(*) runs through all groups on G that are different from G(∘). Similarly, if G(*) runs through all groups on G that are not isomorphic to G(∘), then the minimum of dist(G(∘), G(*)) will be denoted by v(G(∘)).
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- Groups St Andrews 1997 in Bath , pp. 248 - 252Publisher: Cambridge University PressPrint publication year: 1999