4. (a) Let H be a subgroup of Sn with H not contained in An. Prove that [H: HnAn] =2. (b) Let G be a finite simple group with a subgroup H such that [G: H] = k > 2. Prove that |G| divides.
4. (a) Let H be a subgroup of Sn with H not contained in An. Prove that [H: HnAn] =2. (b) Let G be a finite simple group with a subgroup H such that [G: H] = k > 2. Prove that |G| divides.
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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![4. (a) Let H be a subgroup of Sn with H not contained in An. Prove that
[H: HnAn] =2.
(b) Let G be a finite simple group with a subgroup H such that [G: H] = k > 2.
Prove that G divides.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe469c8e1-3d66-4aef-8026-c4bcbe49028e%2Fb93c6fd1-0b03-4446-bca3-309d7ef2744f%2F51p122d_processed.png&w=3840&q=75)
Transcribed Image Text:4. (a) Let H be a subgroup of Sn with H not contained in An. Prove that
[H: HnAn] =2.
(b) Let G be a finite simple group with a subgroup H such that [G: H] = k > 2.
Prove that G divides.
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