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Showing 1 to 7 of 7 for “"Isomorphism Type"”.
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SYMMETRIC PRESENTATIONS AND RELATED TOPICS
… and several classical groups. We have given the isomorphism type of each of the group mentioned in the thesis. In each case, a proof of the isomorphism type is provided, either computer-based or by hand. In addition, by hand constructions, using the technique of double coset enumeration, are …
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Homormophic Images and their Isomorphism Types
… homomorphic images that we have discovered, the isomorphism type of each group is given. The homomorphic images discovered include Linear groups, Alternating groups, and two sporadic simple groups J<sub>1</sub> and J<sub>2</sub>X2 where J<sub>1</sub> is the smallest Janko group and J<sub>2</sub> …
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CONSTRUCTIONS AND ISOMORPHISM TYPES OF IMAGES
… proofs, either by hand or computer-based, of the isomorphism type of each image. In addition, we use Iwasawa's Lemma to prove that L<sub>2</sub>(13) over A<sub>5</sub>, L<sub>2</sub>(8) over D<sub>14</sub>, L<sub>2</sub>(13) over D<sub>14</sub>, L<sub>2</sub>(27) over 2D<sub>14</sub>, and …
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Torsion Subgroups Of Rational Elliptic Curves Over Odd Degree Galois Fields
… the possible torsion subgroups based on the isomorphism type of Gal(K/Q). We then determine the possibilities for the growth of torsion from E(Q)_tors to E(K)_tors, i.e. what the possibilities are for E(K)_tors ⊇ E(Q)_tors given a fixed torsion subgroup E(Q)_tors. Extending the techniques …
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Torsion Subgroups of Rational Elliptic Curves Over Odd Degree Galois Fields
… the possible torsion subgroups based on the isomorphism type of Gal(K/Q). We then determine the possibilities for the growth of torsion from E(Q)_tors to E(K)_tors, i.e. what the possibilities are for E(K)_tors ⊇ E(Q)_tors given a fixed torsion subgroup E(Q)_tors. Extending the techniques …
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Homomorphic Images And Related Topics
… developed by Robert T Curtis, is a special type of infinite group formed by a semi-direct product of a free group m<sup>*</sup><sup>n</sup> and a transitive permutation group of degree n. Since progenitors are infinite, we add necessary relations to produce finite homomorphic images. Curtis …
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SYMMETRIC PRESENTATIONS OF NON-ABELIAN SIMPLE GROUPS
… and extension theory to determine groups up to isomorphisms. The progenitor, developed by Robert T. Curtis, is a semi-direct product of the following form: P≅2*<sup>n</sup>: N = {πw | π ∈ N, w a reduced word in the t<sub>i</sub>} where 2*<sup>n</sup> denotes a free product of n copies of the …