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Evans A. — Orthomorphism Graphs of Groups (Lecture Notes in Mathematics)
Evans A. — Orthomorphism Graphs of Groups (Lecture Notes in Mathematics)

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Название: Orthomorphism Graphs of Groups (Lecture Notes in Mathematics)

Автор: Evans A.

Аннотация:

This book is about orthomorphisms and complete mappings of groups, and related constructions of orthogonal latin squares. It brings together, for the first time in book form, many of the results in this area. The aim of this book is to lay the foundations for a theory of orthomorphism graphsof groups, and to encourage research in this area. To this end, many directions for future research are suggested. The material in this book should be accessible to any graduate student who has taken courses in algebra (group theory and field theory). It will mainly be useful in research on combinatorial design theory, group theory and field theory.
Read more at http://ebookee.org/Orthomorphism-Graphs-of-Groups-Lecture-Notes-in-Mathematics-by-Anthony-B-Evans_1127385.html#hLgx5pdakTSDsOfD.99


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1992

Количество страниц: 119

Добавлена в каталог: 17.04.2014

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$(\sigma,\varepsilon)$-systems      27
$(\sigma,\varepsilon)$-systems, equivalence of-      27
$(\sigma,\varepsilon)$-systems, order of      27
$(\sigma,\varepsilon)$-systems, rank of the solution space of-      27
Adjacency of mappings      1
Adjacency of orthomorphisms      2
Affine planes      9—13
Almost simple groups      24
Aschbacher's reduction      24
Automorphisms of left neofields      15—16
Automorphisms of Orth(G)      3—5
Automorphisms, fixed point free-      51—54
Cartesian groups      11
Cartesian planes      11
Cayley tables of groups      6
CIP-neofields      18
Clique numbers of orthomorphism graphs      2
CMP-neofields      18
Collineations of nets      11—12
Commutative left neofields      16—17
Complete mapping polynomials      44
Complete mappings      1
Complete sets of mutually orthogonal Latin squares      7
Complete sets of orthomorphisms      3 73—76
Components of partial congruence partitions      50
Congruences of Orth(G)      3—5
Cyclic neofields      17—18
Cyclotomic orthomorphisms      41—43
Cyclotomy classes      40—41
Cyclotomy numbers      41
Degrees of orthomorphisms      2
Degrees of partial congruence partitions      50
Desarguesian affine planes      10
Designs, Knut Vic-      62—63
Designs, resolvable transversal-      9—11
Designs, transversal-      9—11
Difference families, $(\nu,k,1)$      65—66
Difference families, $(\nu,k,1;H)$      66—67
Difference matrices      7—8 67—68
Difference sets, $(\nu,k,1)$      63—64
Difference sets, $(\nu,k,1;H)$      64—65
Direction of a translation of a net      11
Duals of complete sets of orthomorphisms      13
Equivalence of $(\sigma,\varepsilon)$-systems      27
Exchange inverse property of a left neofield      16—17
Exdomain elements of near orthomorphisms      14
Fixed point free automorphisms      51 52 54
Generalized Hadamard matrices      8—9 74
Hermite's criterion      44
Homologies of near orthomorphisms      16
Homologies of Orth(G)      3—5
HP-systems      24
Inverse property of a left neofield      16—17
Inversions of Orth(G)      3—5
Knut Vic designs      62—63
Latin squares      6—7 62
Latin squares, Based on groups      6
Latin squares, complete sets of mutually orthogonal—      7
Latin squares, maximal sets of mutually orthogonal—      7 67—73
Latin squares, orthogonality of-      6
Left inverse property of a left neofield      16—17
Left neofields      14—17
Linear orthomorphisms      35—36 38—41
LXP-neofields      18
Maximal difference matrices      8 67—68
Maximal sets of mutually orthogonal Latin squares      7 67—73
Mutually orthogonal Latin squares based on groups      6
Near orthomorphisms      14—17
Neighbors of orthomorphisms      2
Neofields      14—18
Neofields, CIP-      18
Neofields, CMP-      18
Neofields, Commutative left-      16—17
Neofields, cyclic-      17—18
Neofields, exchange inverse property of left-      16—17
Neofields, inverse property of left-      16—17
Neofields, left inverse property of left-      16—17
Neofields, left-      14—17
Neofields, LXP-      18
Neofields, order of of left-      14
Neofields, presentation function of of left-      14—15
Neofields, right inverse property of left-      16—17
Neofields, RXP-      18
Neofields, XIP-      18
Neofields, XMP-      18
Nets      9—12
Nets, collineations of-      11—12
Nets, direction of a translation of a-      11
Nets, Splitting translation-      50
Nets, translation-      50 52
Nets, translations of-      11
Normalized permutation polynomials      45—46
Order of $(\sigma,\varepsilon)$-systems      27
Order of a representation of a graph      59
Order of left neofields      14
Orth(G)      2
Orthogonal Latin square graphs      59
Orthogonal mappings      1
Orthogonality of Latin squares      6
Orthomorphism graphs of groups      2
Orthomorphism graphs of groups, clique numbers of-      2
Orthomorphism graphs of groups, r-cliques of-      2
Orthomorphism polynomials      44—47 49 71 79—82
Partial congruence partitions      50
Partial congruence partitions, components of-      50
Partial congruence partitions, degrees of-      50
Permutation polynomials      44—46 48
Permutation polynomials, normalized-      45—46
Permutations of groups      1
Planes, affine-      9—13
Planes, Cartesian-      11 73
Planes, desarguesian-      10
Planes, projective-      9
Polynomials, complete mapping-      44 49
Polynomials, normalized permutation-      45—46
Polynomials, orthomorphism-      44—47 49 71 79—82
Polynomials, Permutation-      44—46 48
Presentation functions of left neofields      14—15
Projective planes      9
Qrthomorphisms      1
Qrthomorphisms, adjacency of-      2
Qrthomorphisms, complete sets of-      3 73—76
Qrthomorphisms, cyclotomic-      41—43 47—49
Qrthomorphisms, degrees of-      2
Qrthomorphisms, duals of complete sets of-      13
Qrthomorphisms, linear-      35—36 38—41
Qrthomorphisms, near-      14—17
Qrthomorphisms, neighbors of-      2
Qrthomorphisms, quadratic-      36—41 48 71—72 75—76
Quadratic orthomorphisms . . .      36—41 48 71—72 75—76
Quasisimple groups      24
r-cliques of orthomorphism graphs      2
Rank of the solution space of a $(\sigma,\varepsilon)$-system      27
Reflections of Orth(G)      3—5
Representations of graphs      58—59
Resolvable transversal designs      9—11
Right inverse property of a left neofield      16—17
RXP-neofields      18
Splitting translation nets      50
Starters      1
Strong complete mappings      60—62
The orthomorphism graph of a group, Orth(G)      2
The orthomorphism graph of a group, Orth(G), automorphisms of-      3—5
The orthomorphism graph of a group, Orth(G), congruences of-      3—5
The orthomorphism graph of a group, Orth(G), inversions of-      3—5
The orthomorphism graph of a group, Orth(G), reflections of-      3—5
The orthomorphism graph of a group, Orth(G), translations of-      3—5
Translation nets      50 52
Translations of nets      11
Translations of Orth(G)      3—5
Transversal designs      9—11
Transversal designs, resolvable-      9—11
XIP-neofields      18
XMP-neofields      18
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