Characteristically polycyclic group
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This article defines a group property: a property that can be evaluated to true/false for any given group, invariant under isomorphism
View a complete list of group properties
VIEW RELATED: Group property implications | Group property non-implications |Group metaproperty satisfactions | Group metaproperty dissatisfactions | Group property satisfactions | Group property dissatisfactions
Contents
Definition
A group is termed characteristically polycyclic if there exists a characteristic series (i.e., a subgroup series where all the subgroups are characteristic) of finite length for the group, such that all the factor groups are cyclic groups.
Relation with other properties
Stronger properties
Weaker properties
Facts
References
Journal references
- Groups with a characteristic cyclic series by John R. Durbin and Merry McDonald, Journal of Algebra, ISSN 00218693, Volume 18, Page 453 - 460(Year 1971): ^{PDF (ScienceDirect)}^{More info}