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• W2896492727 abstract "The dominant theme of this thesis is the construction of matrix representations of finite solvable groups using a suitable system of For a finite solvable group $G$ of order $N = p_{1}p_{2}dots p_{n}$, where $p_{i}$'s are primes, there always exists a subnormal series: $langle {e} rangle = G_{o} < G_{1} < dots < G_{n} = G$ such that $G_{i}/G_{i-1}$ is isomorphic to a cyclic group of order $p_{i}$, $i = 1,2,dots,n$. Associated with this series, there exists a system of generators consisting $n$ elements $x_{1}, x_{2}, dots, x_{n}$ (say), such that $G_{i} = langle x_{1}, x_{2}, dots, x_{i} rangle$, $i = 1,2,dots,n$, which is called a long system of generators. In terms of this system of generators and conjugacy class sum of $x_{i}$ in $G_{i}$, $i = 1,2, dots, n$, we present an algorithm for constructing the irreducible matrix representations of $G$ over $mathbb{C}$ within the group algebra $mathbb{C}[G]$. This algorithmic construction needs the knowledge of primitive central idempotents, a well defined set of primitive (not necessarily central) idempotents and the diagonal subalgebra of $mathbb{C}[G]$. In terms of this system of generators, we give simple expressions for the primitive central idempotents, a well defined system of primitive (not necessarily central) idempotents and a convenient set of generators of the diagonal subalgebra of $mathbb{C}[G]$. For a finite abelian group, we present an algorithm for constructing the inequivalent irreducible matrix representations over a field of characteristic $0$ or prime to the order of the group and a systematic way of computing the primitive central idempotents of the group algebra. Besides that, we give simple expressions of the primitive central idempotents of the rational group algebra of a finite abelian group using a long presentation and it's Wedderburn decomposition." @default.
• W2896492727 created "2018-10-26" @default.
• W2896492727 creator A5040631447 @default.
• W2896492727 date "2018-10-06" @default.
• W2896492727 modified "2023-09-27" @default.
• W2896492727 title "Algorithmic construction of representations of finite solvable groups" @default.
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• W2896492727 hasPublicationYear "2018" @default.
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