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- Cycle_graph_(algebra) abstract "In group theory, a sub-field of abstract algebra, a group cycle graph illustrates the various cycles of a group and is particularly useful in visualizing the structure of small finite groups. For groups with fewer than 16 elements, the cycle graph determines the group (up to isomorphism).A cycle is the set of powers of a given group element a; where an, the n-th power of an element a, is defined as the product of a multiplied by itself n times. The element a is said to generate the cycle. In a finite group, some non-zero power of a must be the group identity, e; the lowest such power is the order of the cycle, the number of distinct elements in it. In a cycle graph, the cycle is represented as a polygon, with the vertices representing the group elements, andthe connecting lines indicating that all elements in that polygon are members of the same cycle.".
- Cycle_graph_(algebra) thumbnail Dih4_cycle_graph.svg?width=300.
- Cycle_graph_(algebra) wikiPageExternalLink CycleGraph.html.
- Cycle_graph_(algebra) wikiPageID "1681010".
- Cycle_graph_(algebra) wikiPageRevisionID "587027274".
- Cycle_graph_(algebra) hasPhotoCollection Cycle_graph_(algebra).
- Cycle_graph_(algebra) subject Category:Abstract_algebra.
- Cycle_graph_(algebra) subject Category:Application-specific_graphs.
- Cycle_graph_(algebra) subject Category:Group_theory.
- Cycle_graph_(algebra) comment "In group theory, a sub-field of abstract algebra, a group cycle graph illustrates the various cycles of a group and is particularly useful in visualizing the structure of small finite groups. For groups with fewer than 16 elements, the cycle graph determines the group (up to isomorphism).A cycle is the set of powers of a given group element a; where an, the n-th power of an element a, is defined as the product of a multiplied by itself n times. The element a is said to generate the cycle.".
- Cycle_graph_(algebra) label "Cycle graph (algebra)".
- Cycle_graph_(algebra) label "Graphe des cycles".
- Cycle_graph_(algebra) label "巡回グラフ".
- Cycle_graph_(algebra) label "環圖".
- Cycle_graph_(algebra) sameAs Graphe_des_cycles.
- Cycle_graph_(algebra) sameAs 巡回グラフ.
- Cycle_graph_(algebra) sameAs m.05mxyg.
- Cycle_graph_(algebra) sameAs Q1012802.
- Cycle_graph_(algebra) sameAs Q1012802.
- Cycle_graph_(algebra) wasDerivedFrom Cycle_graph_(algebra)?oldid=587027274.
- Cycle_graph_(algebra) depiction Dih4_cycle_graph.svg.
- Cycle_graph_(algebra) isPrimaryTopicOf Cycle_graph_(algebra).
