Article
Licensed
Unlicensed
Requires Authentication
Local characterization of non-finitary locally finite simple groups
-
Stefaan Delcroix
Published/Copyright:
July 16, 2008
Abstract
In this paper, we prove that if G is a non-finitary locally finite, simple group then the following holds:
G is of p-type for some prime p if and only if G is not finitary and there exist a prime q ≠ p and x ∈ G such that |x| is a power of q and 〈xQ〉 is abelian for all q-subgroups Q of G containing x.
G is of alternating type if and only if for any prime p and any x ∈ G with |x| a power of p, there exists a p-subgroup P of G containing x such that 〈xP〉 is not solvable.
Received: 2007-03-23
Revised: 2007-04-09
Published Online: 2008-07-16
Published in Print: 2008-July
© de Gruyter 2008
You are currently not able to access this content.
You are currently not able to access this content.
Articles in the same Issue
- Intransitive geometries and fused amalgams
- On intersections of classical groups
- A characterization of Aut(G2(3))
- The expected order of a random unitary matrix
- On the exponent semigroups of finite p-groups
- On hypercentral factor groups from certain classes
- Local characterization of non-finitary locally finite simple groups
- Less than continuum many translates of a compact nullset may cover any infinite profinite group
- Hausdorff dimension of some groups acting on the binary tree
- The mean Dehn functions of abelian groups
Articles in the same Issue
- Intransitive geometries and fused amalgams
- On intersections of classical groups
- A characterization of Aut(G2(3))
- The expected order of a random unitary matrix
- On the exponent semigroups of finite p-groups
- On hypercentral factor groups from certain classes
- Local characterization of non-finitary locally finite simple groups
- Less than continuum many translates of a compact nullset may cover any infinite profinite group
- Hausdorff dimension of some groups acting on the binary tree
- The mean Dehn functions of abelian groups
