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=13964
Suzuki-2-group. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Suzuki-2-group&oldid=13964
This article was adapted from an original article by V.D. Mazurov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article