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DC Field | Value | Language |
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dc.contributor.advisor | Shankar, B R | - |
dc.contributor.author | Sahu, Sehra | - |
dc.date.accessioned | 2024-05-16T05:45:00Z | - |
dc.date.available | 2024-05-16T05:45:00Z | - |
dc.date.issued | 2023 | - |
dc.identifier.uri | http://idr.nitk.ac.in/jspui/handle/123456789/17757 | - |
dc.description.abstract | Explicit 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.iso | en | en_US |
dc.publisher | National Institute Of Technology Karnataka Surathkal | en_US |
dc.subject | Galois Group | en_US |
dc.subject | Multi-Quadratic Extension | en_US |
dc.subject | Cyclotomic Extension | en_US |
dc.subject | Residue Pattern | en_US |
dc.title | Galois Group of Certain Algebraic Extensions and Their Relations With Primes In Arithmetic Progression | en_US |
dc.type | Thesis | en_US |
Appears in Collections: | 1. Ph.D Theses |
Files in This Item:
File | Description | Size | Format | |
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177081-MA004-SEHRA SAHU.pdf | 4.18 MB | Adobe PDF | View/Open |
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