Logo
Home Study Material Contact Search
AI Chat FREE
  1. mathematics
  2. advance math
  3. prove that there is only one possible multiplicati

Prove that there is only one possible multiplication table for G if G has exactly 1,...

60.2K

Verified Solution

Question

Advance Math

  1. Prove that there is only one possible multiplication table forG if G has exactly 1, 2, or 3 elements. Analyze the possiblemultiplication tables for groups with exactly 4 elements, and showthat there are two distinct tables, up to reordering the elementsof G. Use these tables to prove that all groups with < 4elements are commutative.

(You are welcome to analyze groupswith 5 elements using the same technique, but you will soon knowenough about groups to be able to avoid such brute-forceapproaches.)

Answer & Explanation Solved by verified expert
3.8 Ratings (518 Votes)
If G has exactly one element say then we must have the groupidentity and so the table is    See Answer
Get Answers to Unlimited Questions

Join us to gain access to millions of questions and expert answers. Enjoy exclusive benefits tailored just for you!

Membership Benefits:
  • Unlimited Question Access with detailed Answers
  • Zin AI - 3 Million Words
  • 10 Dall-E 3 Images
  • 20 Plot Generations
  • Conversation with Dialogue Memory
  • No Ads, Ever!
  • Access to Our Best AI Platform: Zin AI - Your personal assistant for all your inquiries!
Become a Member

Other questions asked by students

Q

Foreign Currency ImpactKellogg included the following note in its fiscal 2015 10-Kreport ($ millions)....Foreign...

Accounting
Q

the patellar knee-jerk reflex tests. Which nerve carries the afferent (sensory) signal? Which nerve carries the efferent...

Medical Sciences
Q

Access the article entitled “Biofeedback: Listen to the body” written by Alexander and Steefel (1995). After...

Psychology
Q

      Design an algorithm for each of the exercises and type it into a word document....

Electrical Engineering
Q

Think about some of your own \"socialization\" experiences. Describe one event, experience, or factor that you...

Psychology
Q

calculate the work done when: a) a 55 N force acting at an angle of 28...

Physics
Q

Which of the following statements about resting membrane potential is TRUE A The resting membrane...

Biology
Q

A sphere P of mass m and velocity undergoes an oblique and perfectly elastic collision...

Physics
Q

Evaluate the definite integral by interpreting it in terms of areas 3x 12 dx

Calculus
Q

5 Solve the following equation

Algebra
Q

Shield Company has total proceeds from sales of $4,515. If the proceeds include sales tax...

Accounting
Q

Mario is a fireman at your fire department. He contribute to his employer's retirement. saving...

Accounting