On the Structure of Frobenius Groups
- 1 January 1957
- journal article
- Published by Canadian Mathematical Society in Canadian Journal of Mathematics
- Vol. 9, 587-596
- https://doi.org/10.4153/cjm-1957-067-8
Abstract
Let G be a group which has a faithful representation as a transitive permutation group on m letters in which no permutation other than the identity leaves two letters unaltered, and there is at least one permutation leaving exactly one letter fixed. It is easily seen that if G has order mh, a necessary and sufficient condition for G to have such a representation is that G contains a subgroup H of order h which is its own normalizer in G and is disjoint from all its conjugates. Such a group G is called a Frobenius group of type (h, m).Keywords
This publication has 3 references indexed in Scilit:
- On a conjecture of FrobeniusProceedings of the American Mathematical Society, 1956
- Über Lie’sche Ringe mit PrimzahlcharakteristikAbhandlungen aus dem Mathematischen Seminar der Universitat Hamburg, 1939
- Über endliche FastkörperAbhandlungen aus dem Mathematischen Seminar der Universitat Hamburg, 1935