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Elements of linear representation of finite groups.

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dc.contributor.author Harned, Daniel J.
dc.date.accessioned 2012-06-20T19:39:10Z
dc.date.available 2012-06-20T19:39:10Z
dc.date.created 1990 en_US
dc.date.issued 2012-06-20
dc.identifier.uri http://hdl.handle.net/123456789/1348
dc.description 91 leaves en_US
dc.description.abstract This paper is a survey of elementary concepts of the theory of representation of finite groups; wherein abstract groups are realized as groups of linear transformations or matrices. Basic definitions and examples of the above are given, as well as a notion of an equivalence relation for representations. The regular representation is presented through the concept of a group algebra. Other properties, such as sub-representations and irreducible representations, lead to an important result about the reducibility of representations of subgroups known as Clifford's Theorem. The character of a representation is then defined as the trace of the linear transformation or matrix which represents each element of the group. The relationship between characters and representations is developed including: (1) orthogonality relations from Schur's Lemma; and (2) the fact that the number of irreducible representations of a group is equal to its number of conjugacy classes. Finally, the concepts of induced representations and characters are explored, culminating in the Frobenius reciprocity formula. en_US
dc.language.iso en_US en_US
dc.subject Finite groups. en_US
dc.subject Modules (Algebra). en_US
dc.title Elements of linear representation of finite groups. en_US
dc.type Thesis en_US
dc.college las en_US
dc.advisor Essam A. Abotteen en_US
dc.department mathematics, computer science, and economics en_US

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