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Classification of groups of small orders

Anja Smrtnik (2013) Classification of groups of small orders. Diploma thesis.

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    Abstract

    In the present BsC thesis we deal with algebraic structures, called groups. A group is a set closed under a binary operation which is associative, has an identity and in which each element has an inverse. Groups are usually studied up to group isomorphisms. Using basic results of group theory, encountered during our undergraduate studies, we classify all groups of small orders up to order 23, with the exception of groups of order 16, of course only up to isomorphism of groups. We determine how many groups of a particular order there are and name them. Furthermore, we also determine the number of elements of each possible order. We present all nonstandard groups as groups of corresponding permutations for which a corresponding multiplication table is written.

    Item Type: Thesis (Diploma thesis)
    Keywords: group, finite group, order of a group, isomorphism of groups, Sylow theorems, classification of groups, group table
    Number of Pages: 59
    Language of Content: Slovenian
    Mentor / Comentors:
    Mentor / ComentorsIDFunction
    doc. dr. Primož ŠparlMentor
    Link to COBISS: http://www.cobiss.si/scripts/cobiss?command=search&base=50126&select=(ID=9678409)
    Institution: University of Ljubljana
    Department: Faculty of Education, Faculty of Mathematics and Physics
    Item ID: 1575
    Date Deposited: 04 Jul 2013 14:22
    Last Modified: 04 Jul 2013 14:22
    URI: http://pefprints.pef.uni-lj.si/id/eprint/1575

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