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
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].](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7472f4ab-d14f-478a-9e76-acd1247f1b6d%2F2e4c993e-8dd9-44a3-86b4-c2ec9a724a16%2Flxp76xh_processed.jpeg&w=3840&q=75)
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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