Namespaces
Variants
Actions

Suzuki-2-group

From Encyclopedia of Mathematics
Revision as of 17:06, 7 February 2011 by 127.0.0.1 (talk) (Importing text file)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to: navigation, search

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
This article was adapted from an original article by V.D. Mazurov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article