Publication: Resultados sobre determinación de grupos por su orden y el de sus elementos
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2019
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Abstract
En este trabajo determinamos los posibles grupos a los que un grupo puede ser isomorfo una vez se ha fijado su orden o especificado el de alguno de sus elementos, haciendo uso de métodos elementales de teoría de grupos en el manejo de tres herramientas: el producto semidirecto, las extensiones de grupos y los grupos de automorfismos de algunas de las familias más conocidas. En los primeros tres capítulos expondremos dichas herramientas, y en los siguientes determinamos los grupos de orden p, p2, p3, 2p, 4p, pq y 2k cuando el grupo tiene un elemento de orden k.
In this work we determine possible groups which a group can be isomorphic to, once its order has been fixed or one of its elements specified, using elementary methods of group theory in the management of three tools: semidirect products, group extensions and automorphism groups of some of the best known families. In the first three chapters we will expose these tools, and in the following ones we determine all groups of order p, p2, p3, 2p, 4p, pq and 2k when the group has an element of order k.
In this work we determine possible groups which a group can be isomorphic to, once its order has been fixed or one of its elements specified, using elementary methods of group theory in the management of three tools: semidirect products, group extensions and automorphism groups of some of the best known families. In the first three chapters we will expose these tools, and in the following ones we determine all groups of order p, p2, p3, 2p, 4p, pq and 2k when the group has an element of order k.
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