Hypercentre
From Encyclopedia of Mathematics
A member 
of the upper central series of a group 
. The first hypercentre 
is the centre of the group (cf. Centre of a group); if all 
, 
, are known, then 
if 
is a limit ordinal number; 
is the complete pre-image of the centre of the quotient group 
if 
is a non-limit ordinal number. The hypercentres of a group are locally nilpotent.
Comments
References
| [a1] | D.J.S. Robinson, "Finiteness condition and generalized soluble groups" , 1–2 , Springer (1972) |
How to Cite This Entry:
Hypercentre. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Hypercentre&oldid=17756
Hypercentre. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Hypercentre&oldid=17756
This article was adapted from an original article by V.M. Kopytov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article