Theory of Groups of Finite Order

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Courier Corporation, 2004 - Mathematics - 512 pages
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After introducing permutation notation and defining group, the author discusses the simpler properties of group that are independent of their modes of representation; composition-series of groups; isomorphism of a group with itself; Abelian groups; groups whose orders are the powers of primes; Sylow's theorem; more. 18 illustrations. A classic introduction.
 

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Contents

CHAPTER I
1
Transpositions representation of a permutation as
11
Various modes of representing groups
24
CHAPTER IV
46
ON THE COMPOSITIONSERIES OF A GROUP
64
CHAPTER VI
81
CHAPTER VIII
119
CHAPTER IX
149
Set of groupcharacteristics in conjugate repre
293
CHAPTER XVIII
372
the generating operations are of finite order 389394
389
CHAPTER XIX
402
CHAPTER XX
428
Examples 457459
460
On the completely reduced form of a group
470
NOTE F On groups of finite order which are simply iso
476

Conjugate permutations are similar selfconjugate
173
CHAPTER XII
231
CHAPTER XIII
243
Characteristic equation of a substitution charac
250
CHAPTER XIV
269
CHAPTER XV
280
NOTE H On the group of the twentyseven lines on
485
NOTE J On conditions for the finiteness of the order of
491
On the groupcharacteristics of the fractional linear
499
INDEX OF TECHNICAL TERMS
507
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