For each of the following values of ∆, find all elements of the ideal class group of G=C_(delta) discriminant ∆ and determine the invariant factor type of G. Find a generator or set of generators for G, and demonstrate that each element of G can be written as a power of that generator, or as a product of powers of the generators. Show your work and explain your calculations. a. delta=-151 b.delta=244
For each of the following values of ∆, find all elements of the ideal class group of G=C_(delta) discriminant ∆ and determine the invariant factor type of G. Find a generator or set of generators for G, and demonstrate that each element of G can be written as a power of that generator, or as a product of powers of the generators. Show your work and explain your calculations. a. delta=-151 b.delta=244
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter3: Groups
Section3.4: Cyclic Groups
Problem 27E
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For each of the following values of ∆, find all elements of the ideal class group of G=C_(delta) discriminant ∆ and determine the invariant factor type of G. Find a generator or set of generators for G, and demonstrate that each element of G can be written as a power of that generator, or as a product of powers of the generators. Show your work and explain your calculations.
a. delta=-151
b.delta=244
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