[GAP Forum] Request

[muniru asiru]

Sirs,

I should be grateful if someone would help me this problem fron Group Theory.
 
If G is a group of order $p$ writeen additively, and $a$ is an element of G, then 
there is an element $b$ in G such that 
 
1.  $(a+b) mod p =1$.  
 
2.  $(a+b) mod p =p$. 
 
What name do we call the elements $a$ and $b$ in Group Theory and in Gap in each case?
 
Thanks.


Dr. Muniru A. Asiru,
Department of Mathematics & Statistics, 
The Federal Polytechnic, 
P.M.B. 55, 
Bida, 
Niger State, 
Nigeria.

OR

Dr. Muniru A. Asiru,
P.O.Box. 294, 
Bida, 
Niger State, Nigeria.

Email Addresses: 
maasiru at yahoo.com, 
remiasiru at yahoo.com, 

Mobile Phone number: +2348034271010