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Polites G.W. — An Introduction to the Theory of Groups
Polites G.W. — An Introduction to the Theory of Groups

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Название: An Introduction to the Theory of Groups

Автор: Polites G.W.


It is to be emphasized that this book is intended as an introduction to the theory of groups. It is hoped that a reading of this book will create a great deal of interest in the subject of groups, and that the reader will prolong this interest by continued reading in many of the fine books that go into the theory in much more depth. It is to be emphasized, too, that familiarity with and a knowledge of most of the material here is essential to a further study and understanding of the more advanced topics and specialized material on group theory.

The primary motive for the writing of the book was to provide a text for the study of groups by students engaged in independent study or honors work. It should also do very nicely for use in a special-topics course in mathematics, or in a mathematics seminar. It is directed mainly to the advanced undergraduate student and should provide enough material for a three-credit-hour course. The book also may have appeal for many graduate students as a reference, or as a supplement to a text in abstract algebra.

Finally, it should be stressed that most of the exercises in this book are of extreme importance and should be studied closely. Many results found later on in the text depend strongly on exercises that may occur much earlier. The examples also should be carefully noted, and the reader should try to construct others in addition to solving the ones given.

Язык: en

Рубрика: Математика/Алгебра/Теория групп/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1968

Количество страниц: 80

Добавлена в каталог: 12.12.2004

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Предметный указатель
Abelian group      3
Adjunction of an element to a field      64
Alternating group      27
Ascending central series      45
Automorphism of a field      70
Automorphism of a group      21
Basis      66
Binary operation      1
Cayley’s Theorem      13
Center of a group      15
Central series      44
Characteristic O      70
Class of a nilpotent group      44
Commutator      15
Commutator, subgroup      15
COMPLEX      14
Composition, factors      29
Composition, series      29
Conjugate, elements      22
Conjugate, subgroups      13
Coset      7
CYCLE      25
Cyclic group      8
Degree of a polynomial      65
Degree of an extension      67
Derived group      15
Direct product      33—34
Double coset      38
Euler phi-function      11
Even permutation      26
Extension field      64
Factor group      19
Field      63
Field of quotients      65
Field of rational functions      65
Finite dimensional      66
Finite extension      67
Fixed field      70
Frattini subgroup      47
Fundamental Theorem of Galois Theory      73
Galois field      64
Galois group      73
General polynomial of degree n      76
Group, definitions of      1—3
Hamiltonian group      56
Homomorphic image      17
Homomorphism      16—17
Index of a subgroup      8
Inner automorphism      22
Invariant subgroup      14
Irreducible polynomial      68
Isomorphic normal series      29—30
Isomorphism of a field      70
Isomorphism of a group      12
Jordan — Holder theorem      31
Kernel      17—18
Klein four-group      49—50
Lagrange’s Theorem      8
linear combination      66
Linearly dependent vectors      66
Mapping      1
Maximal normal subgroup      27
Multiplicity      68
Natural homomorphism      20
Nilpotent group      44—45
Normal extension      73
Normal series      29
Normal subgroup      13
normalizer      14
Odd permutation      26
One-to-one mapping      4—5
Onto mapping      5
Order of a group      8
Order of an element      9
Outer automorphism      22
p-group      40
Permutation      4
Polynomial      65
Quaternion group      54—55
Quotient group      19
Relatively prime      11
Ring      65
Root of a polynomial      68
Simple group      27
Solvable by radicals      75—76
Solvable, group      32
Splitting field      69—70
Subfield      64
Subgroup      6
Sylow, p-subgroup      42
Sylow, theorems      42—43
Symmetric group      4
Transposition      26
Vector space      65
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