Article contents
On loops which have dihedral 2-groups as inner mapping groups
Published online by Cambridge University Press: 17 April 2009
Abstract
In this paper we consider the situation that a group G has a subgroup H which is a dihedral 2-group and with connected transversals A and B in G. We show that G is then solvable and moreover, if G is generated by the set A ∪ B, then H is subnormal in G. We apply these results to loop theory and it follows that if the inner mapping group of a loop Q is a dihedral 2-group then Q is centrally nilpotent.
- Type
- Research Article
- Information
- Copyright
- Copyright © Australian Mathematical Society 1995
References
- 6
- Cited by