Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
Dr. A Sacidi Group structures, University of Limpopo, 2022 (1) Let G be a group of order pm where P is a prime and (p, m) = 1. Prove that if p > m, then G is not simple. (2) Let G be a simpl

Dr. A Sacidi Group structures, University of Limpopo, 2022 (1) Let G be a group of order pm where P is a prime and (p, m) = 1. Prove that if p > m, then G is not simple. (2) Let G be a simpl

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter4: More On Groups
Section4.6: Quotient Groups
Problem 23E
See similar textbooks
icon
Related questions
Question
PROBLEMS IN GROUP THEORY: SYLOW SUBGROUPS Dr. A Sacidi Group structures, University of Limpopo, 2022 (1) Let G be a group of order pm where P is a prime and (p, m) = 1. Prove that if p > m, then G is not simple. (2) Let G be a simple group. (a) Prove that if G is abelian then |G| = p. (b) Prove that if G is a p-group then |G| = p. (3) Let G be a group of order 2 x pk. Prove that G is not simple. (4) Let G be group of ordr 12. Prove that G is not simple. (5) Let G be group of ordr 24. (6) Let G be group of ordr 30. (7) Let G be group of ordr 40. (8) Let G be group of ordr 45. (9) Let G be group of ordr 48. Prove that G is not simple. Prove that G is not simple. Prove that G is not simple. Prove that G is not simple. Prove that G is not simple. (10) Let G be group of ordr 56. Prove that G is not simple. (11)¹ Let G be a group of order 36.Prove that G is not simple. (12) Let G be a group of order less than 60. Prove that G is simple.
Transcribed Image Text:PROBLEMS IN GROUP THEORY: SYLOW SUBGROUPS Dr. A Sacidi Group structures, University of Limpopo, 2022 (1) Let G be a group of order pm where P is a prime and (p, m) = 1. Prove that if p > m, then G is not simple. (2) Let G be a simple group. (a) Prove that if G is abelian then |G| = p. (b) Prove that if G is a p-group then |G| = p. (3) Let G be a group of order 2 x pk. Prove that G is not simple. (4) Let G be group of ordr 12. Prove that G is not simple. (5) Let G be group of ordr 24. (6) Let G be group of ordr 30. (7) Let G be group of ordr 40. (8) Let G be group of ordr 45. (9) Let G be group of ordr 48. Prove that G is not simple. Prove that G is not simple. Prove that G is not simple. Prove that G is not simple. Prove that G is not simple. (10) Let G be group of ordr 56. Prove that G is not simple. (11)¹ Let G be a group of order 36.Prove that G is not simple. (12) Let G be a group of order less than 60. Prove that G is simple.
Expert Solution
steps

Step by step

Solved in 2 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Elements Of Modern Algebra
Elements Of Modern Algebra
Algebra
ISBN:
9781285463230
Author:
Gilbert, Linda, Jimmie
Publisher:
Cengage Learning,
SEE MORE TEXTBOOKS