
Abstract Algebra Abstract Algebra Math Forum 
 LinkBack  Thread Tools  Display Modes 
October 19th, 2016, 01:51 PM  #1 
Newbie Joined: Oct 2016 From: USA Posts: 2 Thanks: 0  Prove function is cyclic with generator help
How do I show that the group is cyclic with generator Θ(g). Θ(G)={Θ(x) x∈G} if: G and G′ be groups and let Θ : G → G′be a homomorphism. Assume G is cyclic with generator g . 
October 23rd, 2016, 03:21 AM  #2 
Math Team Joined: Jan 2015 From: Alabama Posts: 2,489 Thanks: 630 
Do you mean: "if G is a cyclic group. with generator g, and there exist a homomorphism Θ such that G'= Θ(G), then G' is also cyclic with generator Θ(g)"? As I said in the previous thread, this follows pretty much from the basic definitions. Do you know them? Since you have shown no attempt yourself to do this problem, that is not clear. Do you know what "cyclic" means? Do you know what "homomorphism" means? (And how a "homomorphism" is different from an "isomorphism"?). Write out those definitions and think about how to apply them. 
October 23rd, 2016, 06:08 AM  #3 
Senior Member Joined: Feb 2016 From: Australia Posts: 1,173 Thanks: 386 Math Focus: Yet to find out.  

Tags 
cyclic, function, generator, prove 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
How to prove the following function is increasing function?  Jinliang  Calculus  2  May 12th, 2016 04:30 PM 
Prove AMCD is a cyclic quadrilateral  brhum  Geometry  2  January 25th, 2015 10:24 AM 
Function Generator  krausebj0  Number Theory  1  June 22nd, 2013 01:42 AM 
prove that ( BIOC) cyclic quadrilaterals  MATHS FRIEND  Algebra  13  August 7th, 2012 05:19 PM 
How to prove that 3 is a generator of Zp, p = 17?  asoracc  Abstract Algebra  2  February 27th, 2011 08:03 PM 