(a) Let G be any group. Let H

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter4: More On Groups
Section4.8: Some Results On Finite Abelian Groups (optional)
Problem 16E
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This question investigates properties of subgroups of prime order.
(a) Let G be any group. Let H < G and K <G be subgroups with |H|= |K||= p,
where p is prime. Show that either H = K or H NK = {e}.
(b) Given an example of a group G' of order |G'| = mp with p prime and m > p,
such that G' has at least two different subgroups of order p.
Transcribed Image Text:This question investigates properties of subgroups of prime order. (a) Let G be any group. Let H < G and K <G be subgroups with |H|= |K||= p, where p is prime. Show that either H = K or H NK = {e}. (b) Given an example of a group G' of order |G'| = mp with p prime and m > p, such that G' has at least two different subgroups of order p.
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