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Showing 1 to 13 of 13 for “"Coset enumeration"”.
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Homormophic Images and their Isomorphism Types
… In some cases we have used the double coset enumeration tech- nique to construct the images and for all of the 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 …
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SYMMETRIC PRESENTATIONS AND CONSTRUCTIONS
… groups found using the technique of double coset enumeration and found the isomorphic types of the numerous groups that appeared as homorphic images. These include the sympletic group, S_4(5) and the Janko groups, J_2 and J_1 which were found using a variety of different control groups over …
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Progenitors Related to Simple Groups
… x [(3 x L(2,11)):2] using the process of double coset enumeration.</p>
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Homomorphic Images And Related Topics
… different ways, including the process of double coset enumeration, Iwasawa's Lemma, and linear fractional mappings. We will also investigate the various techniques of finding finite images and their corresponding isomorphism types.</p>
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SYMMETRIC PRESENTATIONS OF NON-ABELIAN SIMPLE GROUPS
… simple groups. Then the algorithm for double coset enumeration together with the first isomorphic theorem aids us in proving the homomorphic image of the group we have constructed. After being presented with a group G, we then compute the composition series to solve extension problems. Given a …
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New computational methods for analysing finitely-presented groups
… contexts. The first procedure creates a labelled coset graph which can be used for rewriting and also for finding expressions for subgroup elements in terms of given generators. We use this procedure to find nice generating sets for torsion-free subgroups of finite index in ordinary triangle …
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SYMMETRIC PRESENTATIONS AND RELATED TOPICS
… constructions, using the technique of double coset enumeration, are given for the groups L<sub>2</sub>(11)X3, L<sub>2</sub>(11), PGL<sub>2</sub>(11), S<sub>5</sub>,(A<sub>5</sub>XA<sub>5</sub>):4, A<sub>7</sub>, and 3<sup>7</sup>:L<sub>2</sub>(7).</p>
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CONSTRUCTIONS AND ISOMORPHISM TYPES OF IMAGES
… constructions, by using the technique of double coset enumeration, for some of the images, including M<sub>11</sub> and M<sub>12</sub>. We have given proofs, either by hand or computer-based, of the isomorphism type of each image. In addition, we use Iwasawa's Lemma to prove that …
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Universal completions of the cyclic amalgams of the same type
… \(\frac{z}{zz}\). Thus OUT (S\(_g\))=2. Coset enumeration is one of the basic methods for investigating finitely generated subgroups in finitely presented.. Information are gradually added to a coset, a relation, a subgroup tables and once they are filled in, all cosets have been …
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Simple Groups and Related Topics
… S<sub>5</sub>, by using the technique of double coset enumeration. We will also provide isomorphism types all of the groups that have appeared as finite homomorphic images. We will show that the group L<sub>2</sub>(8) does not satisfy the conditions of Iwasawas Lemma and that the group …
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Symmetric Presentations and Generation
… of each progenitor, either by hand using double coset enumeration or computer based using MAGMA. We have also constructed Cayley graphs of the following groups, 2<sup>5</sup> : <em>S</em><sub>5</sub> over 2<sup><em>∗</em>5</sup> : <em>S</em><sub>5</sub>, <em>P</em><em>S</em><em>L</em>(2<em>, …