Find two elements of maximum order in the group G = Z100 e Z4O Z2.How many such elements are there?The number of abelian groups of order 2ª36 is equal to the number ofabelian groups of order 2°3". Can you generalize this observation?Let G = Z4 O Z4 O Z25 O Z5 O Z7. Find the corresponding "invariantfactor form".

As Z100 has no element of order 100 otherwise it will be cyclic which is not true. So, we consider…

Find two elements of maximum order in the group G = Z100 Z4 O Z2. How many such elements are there? The number of abelian groups of order 2"36 is equal to the number of abelian groups of order 2°3ª. Can you generalize this observation? Let G = Z4 O Z4 O Z25 O Z5 O Z7. Find the corresponding “invariant factor form".

Find two elements of maximum order in the group G = Z100 Z4 O Z2. How many such elements are there? The number of abelian groups of order 2"36 is equal to the number of abelian groups of order 2°3ª. Can you generalize this observation? Let G = Z4 O Z4 O Z25 O Z5 O Z7. Find the corresponding “invariant factor form".

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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