Year: 1969
Type: article
Abstract: It is an iinmediate consequence of this lemma that the recursiveness of the characterization of CCN-groups given in Theorem 10.5 of [1] may be suppressed in all cases. The properties of CCN-groups of order divisible by at most two primes are still under investigation. The difficulty with the remaining cases is that, for a CCN-group of order divisible by at most two primes, it is possible for the subgroup generated by the elements of composite order to be a p-group of nilpotence class two, or for the entire group to consist of elements of prime order yet not be A5. In the first instance, simple conditions to restrict even the p-group to the class of CCN-grotips are at present lacking, and the action of the remaining elements on this subgroup, while easily described, lacks the simplicity of case (iv) of Theorem 1.1, above. (See Theorem 10.5 of [1, p. 306].) The degenerate case of a finite group without elements of com-
Author: Herbert J. Bernstein
Language: English
Topic: Finite Group Theory Research
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W2077011069