Suzuki-2-group
From Encyclopedia of Mathematics
A finite non-Abelian 
-group 
, other than the group of quaternions, which admits a cyclic group of automorphisms 
that acts transitively on the set 
of elements of order 2 of 
. This means that for any two elements 
and 
of 
there is a natural number 
such that 
. In the Suzuki 
-group 
, the set 
and the identity element constitute a subgroup 
that coincides with the centre of 
; the quotient group 
is then elementary Abelian. If the order of 
is equal to 
, then the order of 
is equal to 
or 
.
Suzuki 
-groups have been fully described (see [1]). The name derives from the fact that in a Suzuki group, the Sylow 
-group 
has these properties.
References
| [1] | G. Higman, "Suzuki 2-groups" Ill. J. Math. , 7 : 1 (1963) pp. 79–96 |
How to Cite This Entry:
Suzuki-2-group. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Suzuki-2-group&oldid=32393
Suzuki-2-group. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Suzuki-2-group&oldid=32393
This article was adapted from an original article by V.D. Mazurov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article