Transcription of GROUP PROPERTIES AND GROUP ISOMORPHISM
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GROUP PROPERTIES AND GROUP ISOMORPHISM
GROUP PROPERTIES AND GROUP ISOMORPHISM Evelyn. M. Manalo Mathematics Honors Thesis University of California, San Diego May 25, 2001 Faculty Mentor: Professor John Wavrik Department of Mathematics GROUP PROPERTIES AND GROUP ISOMORPHISM I n t r o d u c t i o n T H E I M P O R T A N C E O F G R O U P T H E O R Y is relevant to every branch of Mathematics where symmetry is studied. Every symmetrical object is associated with a GROUP . It is in this association why groups arise in many different areas like in Quantum Mechanics, in Crystallography, in Biology, and even in Computer Science. There is no such easy definition of symmetry among mathematical objects without leading its way to the theory of groups.
May 25, 2001 · described by its multiplication table, by its generators and relations, by a Cayley graph, as a group of transformations (usually of a geometric object), as a subgroup of a permutation group, or as a subgroup of a matrix group to name a few. This project started when I was asked by my mentor to look at
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