
Abstract Algebra Abstract Algebra Math Forum 
 LinkBack  Thread Tools  Display Modes 
September 30th, 2017, 04:22 AM  #1 
Member Joined: Jan 2015 From: usa Posts: 79 Thanks: 0  $H$ is relatively prime to $[G:H]$
Ineed help to solve the following problem: Let $G$ be a finite group and $H<G$. suppose that $C_G(x)\subset H$ for all $x\in H\backslash\left\{e\right\}.$ Show that $H$ is relatively prime to $[G:H]$. Thanks in advance. Last edited by mona123; September 30th, 2017 at 04:34 AM. 
October 3rd, 2017, 11:23 AM  #2 
Member Joined: Jan 2016 From: Athens, OH Posts: 62 Thanks: 37 
For p a prime, you just need to use 2 elementary properties of a finite p group P. 1. If Q is a proper subgroup of P, $Q\subset N_P(Q)$ 2. If $<1>\neq N$ is a normal subgroup of P, $N\cap Z(P)\neq <1>$ 

Tags 
$gh$, $h$, prime 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Prime software? not gimps or prime grid.  Kosxon  New Users  2  July 20th, 2017 04:08 PM 
Primorial + prime = prime  momo  Number Theory  4  June 3rd, 2017 04:29 PM 
Pythagorean prime in every prime twin  blind887  Algebra  2  April 12th, 2017 03:35 AM 
For every prime (x+y) exist a prime (xy)  M_B_S  Number Theory  59  October 6th, 2014 12:52 AM 
If P is prime imply that a is prime  momo  Number Theory  14  September 26th, 2008 08:21 AM 