Odd index subgroups of units in cyclotomic fields and applications

1981 ◽  
pp. 269-298 ◽  
Author(s):  
R. James Milgram
Keyword(s):  
Cyclotomic Fields ◽  
Odd Index

scholarly journals A GENERALISED KUMMER'S CONJECTURE

2010 ◽  
Vol 52 (3) ◽  
pp. 453-472 ◽  
Author(s):  
M. J. R. MYERS
Keyword(s):  
Natural Number ◽  
Class Numbers ◽  
Cyclotomic Fields ◽  
Rate Of Growth ◽  
Relative Class ◽  
Almost All

AbstractKummer's conjecture predicts the rate of growth of the relative class numbers of cyclotomic fields of prime conductor. We extend Kummer's conjecture to cyclotomic fields of conductor n, where n is any natural number. We show that the Elliott–Halberstam conjecture implies that this generalised Kummer's conjecture is true for almost all n but is false for infinitely many n.

scholarly journals Finite simple exceptional groups of Lie type in which all subgroups of odd index are pronormal

2020 ◽  
Vol 23 (6) ◽  
pp. 999-1016
Author(s):  
Anatoly S. Kondrat’ev ◽  
Natalia V. Maslova ◽  
Danila O. Revin
Keyword(s):  
Simple Groups ◽  
Finite Simple Groups ◽  
Exceptional Groups ◽  
Odd Index ◽  
Groups Of Lie Type

AbstractA subgroup H of a group G is said to be pronormal in G if H and {H^{g}} are conjugate in {\langle H,H^{g}\rangle} for every {g\in G}. In this paper, we determine the finite simple groups of type {E_{6}(q)} and {{}^{2}E_{6}(q)} in which all the subgroups of odd index are pronormal. Thus, we complete a classification of finite simple exceptional groups of Lie type in which all the subgroups of odd index are pronormal.

Regular Cyclotomic Fields

1998 ◽  
pp. 257-268
Author(s):  
David Hilbert
Keyword(s):  
Cyclotomic Fields

scholarly journals Algorithms for solving linear systems over cyclotomic fields

2010 ◽  
Vol 45 (9) ◽  
pp. 902-917 ◽  
Author(s):  
Liang Chen ◽  
Michael Monagan
Keyword(s):  
Linear Systems ◽  
Cyclotomic Fields

scholarly journals On the Hilbert symbol in cyclotomic fields

2002 ◽  
Vol 105 (1) ◽  
pp. 35-49
Author(s):  
Charles Helou
Keyword(s):  
Cyclotomic Fields ◽  
Hilbert Symbol
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