
Abstract Algebra Abstract Algebra Math Forum 
 LinkBack  Thread Tools  Display Modes 
September 14th, 2017, 12:55 PM  #1 
Member Joined: Jan 2015 From: usa Posts: 92 Thanks: 0  Abelinization of a group
I want identify the abelianization $Q_{4n}/Q'_{4n}$ with a familiar group where $Q_{4n}$ is the dicyclic group. Thanks. 
September 16th, 2017, 11:14 AM  #2 
Member Joined: May 2017 From: Russia Posts: 34 Thanks: 5 
Can we regard $\displaystyle Q_{4n}$ as $\displaystyle \langle a,\ x\  \ a^{2n}=e, \ x^2=a^{n}, \ xax^{1}=a^{1} \rangle$ ? https://groupprops.subwiki.org/wiki/Dicyclic_group I think you could try to prove that any commutator of $\displaystyle Q_{4n}$ can be written as $\displaystyle a^{2k},\ k\in\mathbb{N}$. 

Tags 
abelinization, group 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Abelinization of a group  mona123  Algebra  0  September 14th, 2017 10:49 AM 
Last nontrivial group in the derived series of a solvable group  fromage  Abstract Algebra  0  December 4th, 2016 02:39 AM 
Group Theory Proofs, least common multiples, and group operations HELP!  msv  Abstract Algebra  1  February 19th, 2015 11:19 AM 
Group of units of Z/pZ is a cyclic group  sunflower  Abstract Algebra  0  October 15th, 2010 01:20 PM 
fundamental group, free group  mingcai6172  Real Analysis  0  March 21st, 2009 02:35 PM 