If H is a subgroup of G, then the index of H in G, written as (G : H), is the number of left (or right) cosets of H in G, that is , (G : H) = |{gH : g e G }|. Consider G = Z20 with its subgroups H = <4>, and K = <10>. Find (G : H) and (H : K). %3D

If H is a subgroup of G, then the index of H in G, written as (G : H), is the number of left (or right) cosets of H in G, that is , (G : H) = |{gH : g e G }|. Consider G = Z20 with its subgroups H = <4>, and K = <10>. Find (G : H) and (H : K). %3D

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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Question

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If H is a subgroup of G, then the index of H in G,
written as (G : H), is the number of left (or right)
cosets of H in G, that is , (G : H) = |{gH : ge G }|.
Consider G = Z20 with its subgroups H = <4>, and
K = <10>. Find (G : H) and (H : K).
%3D

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