Descent principle in modular Galois theory

Abhyankar, Shreeram S. ; Keskar, Pradipkumar H. (2001) Descent principle in modular Galois theory Proceedings of the Indian Academy of Sciences - Mathematical Sciences, 111 (2). pp. 139-149. ISSN 0253-4142

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We propound a descent principle by which previously constructed equations over GF(qn)(X) may be deformed to have incarnations over GF(q)(X) without changing their Galois groups. Currently this is achieved by starting with a vectorial (= additive)q-polynomial of q-degree m with Galois group GL(m, q) and then, under suitable conditions, enlarging its Galois group to GL(m, qn) by forming its generalized iterate relative to an auxiliary irreducible polynomial of degreen. Elsewhere this was proved under certain conditions by using the classification of finite simple groups, and under some other conditions by using Kantor’s classification of linear groups containing a Singer cycle. Now under different conditions we prove it by using Cameron-Kantor’s classification of two-transitive linear groups.

Item Type:Article
Source:Copyright of this article belongs to Indian Academy of Sciences.
Keywords:Galois Group; Iteration; Transitivity
ID Code:3
Deposited On:07 Sep 2010 11:30
Last Modified:16 May 2016 11:17

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