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1. Show that the automorphism groups of two isomorphic groups are isomorphic. Let G be a group and g E G be an element of finite order. Show that |g| divides Ig], where p, is the inner automorphism of G generated by g. Give an example of a group G and an element gEG for which 1 < løg] < Ig]-

1. Show that the automorphism groups of two isomorphic groups are isomorphic. Let G be a group and g E G be an element of finite order. Show that |g| divides Ig], where p, is the inner automorphism of G generated by g. Give an example of a group G and an element gEG for which 1 < løg] < Ig]-

Advanced Engineering Mathematics
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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1. Show that the automorphism groups of two isomorphic groups are isomorphic. Let G be a group and g E G be an element of finite order. Show that |al divides |g|, where , is the inner automorphism of G generated by g. Give an example of a group G and an element gE G for which 1 < |Pg[ < \g].
Transcribed Image Text:1. Show that the automorphism groups of two isomorphic groups are isomorphic. Let G be a group and g E G be an element of finite order. Show that |al divides |g|, where , is the inner automorphism of G generated by g. Give an example of a group G and an element gE G for which 1 < |Pg[ < \g].
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