Please use this identifier to cite or link to this item: https://idr.l2.nitk.ac.in/jspui/handle/123456789/17757
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dc.contributor.advisorShankar, B R-
dc.contributor.authorSahu, Sehra-
dc.date.accessioned2024-05-16T05:45:00Z-
dc.date.available2024-05-16T05:45:00Z-
dc.date.issued2023-
dc.identifier.urihttp://idr.nitk.ac.in/jspui/handle/123456789/17757-
dc.description.abstractExplicit structure of Galois group of Q( a1 , a2 , ..., an ) over Q was calculated by Karthick Babu and Anirban Mukhopadhyay. Expanding this knowledge, the problem of finding an ex- √ √ √ plicit Galois group of the field extension Q( a1 , a2 , ..., an , ζd ) over Q in terms of its action √ on ζd and ai for 1 ≤ i ≤ n has been studied. Let p be an odd prime. If we have an integer g which generates a subgroup of index t in (Z/pZ)∗ , then we call g to be a t-near primitive root modulo p. Pieter Moree and Min Sha showed that each coprime residue class contains a positive density of primes p not having g as a t-near primitive root. In this note, for a subset {a1 , a2 , . . . , an } of Z \ {0}, we shall prove that each such coprime residue class contains a positive density of primes p such that ai is not a t-near primitive root. Additionally, ai ’s satisfy certain residue pattern modulo p, for 1 ≤ i ≤ n.en_US
dc.language.isoenen_US
dc.publisherNational Institute Of Technology Karnataka Surathkalen_US
dc.subjectGalois Groupen_US
dc.subjectMulti-Quadratic Extensionen_US
dc.subjectCyclotomic Extensionen_US
dc.subjectResidue Patternen_US
dc.titleGalois Group of Certain Algebraic Extensions and Their Relations With Primes In Arithmetic Progressionen_US
dc.typeThesisen_US
Appears in Collections:1. Ph.D Theses

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