The Theory of Groups

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Courier Corporation, 1958 - Mathematics - 265 pages
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Useful, well-written graduate level text designed to acquaint the reader with group-theoretic methods and to demonstrate their usefulness as tools in the solution of mathematical and physical problems. Covers such subjects as axioms, the calculus of complexes, homomorphic mapping, p-group theory and more. Many proofs are shorter and more transparent than older ones.
 

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Contents

ELEMENTS OF GROUP THEORY
1
Investigation of Axioms
9
Cyclic Groups
15
The Concept of Normal Subgroup
23
THE CONCEPT OF HOMOMORPHV
35
Operators and Operator Homomorphies
44
Normal Chains and Normal Series
57
Commutator Groups and Commutator Forms
78
Theorems on Sylow pGroups
138
On the Enumeration Theorems of the Theory of pGroups
153
Hamiltonian Groups
159
The Theorems of Burnside and Grim
169
The Principal Ideal Theorem
176
B Structure Theory and Direct Products A Treatment
188
Free Products and Groups Given by a Set of Generators
217
Further Exercises for Chap Ill
230

On the Groups of an Algebra
84
THE STRUCTURE AND CONSTRUCTION
109
Abelian Groups
117
On the Order Ideal
123
Extension Theory
124
Extensions with Abelian Factor Group
131
E Further Exercises for Chap IV 5
238
G A Theorem of Wielandt An Addendum to Chap IV
245
H Further Exercises for Chap V I
252
AUTHOR INDEX
259
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