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Glite Dictionary
🔄 Cyclic group property 🦠 Infectious stage
metacyclic

metacyclic

9.9
Made from two cyclic groups, one inside the other
  • adjective
  • /ˌmɛtəˈsaɪklɪk/
  • Specialized
: metacíclico
  • A metacyclic group has a cyclic normal subgroup, making its structure easier to analyze.

Examples

  • A metacyclic group can be described as an extension of two cyclic groups.

  • The mathematician proved that every finite metacyclic group is solvable.

  • Understanding metacyclic structures is important in advanced algebra courses.

  • A group is metacyclic.

  • The metacyclic structure of the group simplifies many calculations.

  • The properties of a metacyclic group often simplify the study of algebraic systems.

  • To fully understand the classification of groups, it's essential to study metacyclic groups.

Surface Forms

metacyclic positive

Morphology

metacyclic = cyclic (opaque) = meta + cycle + ic

The form is built from meta- + cyclic + -ic, but the specialized group-theoretic meaning is not recoverable from the parts for an average learner.

Etymology

Metacyclic combines the parts meta- ('after' or 'beyond') and cyclic ('cycle' or 'circle'). Think of it as 'a cycle on top of a cycle': in group theory it means one cyclic group sits inside another so the whole group is built from two cycles.