Elementary Group Theory
Part of the Texts and Monographs in Physics book series (TMP)
This chapter contains a survey of elementary group theory. For applications in later chapters, the high point is the law of homomorphism and the concepts associated with it.
KeywordsThe group axioms Abelian group cyclic group subgroup order isomorphism homomorphism automorphism permutation symmetric group cycle transposition parity alternating group kernel of a homomorphism normal subgroup simple group conjugate elements cosets Lagrange’s theorem factor group law of homomorphism translations inner automorphisms Cayley’s theorem conjugate subgroups simplicity of 퓐5 composition series Jordan-Hölder theorem generators and relations free group free abelian group the word problem space and point groups direct and semidirect product symmorphic space groups
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© Springer-Verlag Inc. 1981