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Groups, in general ... is called the cyclic subgroup generated by a. The group G is called a cyclic group if there exists an element a G such that G=<a>. In this case a is called a generator of G.
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www.math.niu.edu/~beachy/aaol/groups.html
www.math.niu.edu/~beachy/aaol/groups.html
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Fundamental theorem of cyclic groups - Wikipedia, the free encyclopedia
In abstract algebra, the fundamental theorem of cyclic groups states that every subgroup of a cyclic group is cyclic. Moreover, the order of any subgroup of a cyclic group G\, of order n\, is a ...
en.wikipedia.org/wiki/Fundamental_theorem_of_cyclic_gro...
en.wikipedia.org/wiki/Fundamental_theorem_of_cyclic_groups
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The Medscape Journal ... Journals & Reference ... All Sources Medscape eMedicine MEDLINE Drug Reference...
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www.medscape.com/medline/abstract/12816527
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These are the first steps toward a wider structure-activity relationship for cADPR, and this is the first study to implicate a crucial role for the adenosine ribose hydroxyl groups of cADPR in the biological activity of this cyclic nucleotide.
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www.medscape.com/medline/abstract/9235996
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so cyclic groups of the same order are always isomorphic (Scott 1987, p. 34; Shanks 1993, p. 74). Furthermore, subgroups of cyclic groups are cyclic, ...
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mathworld.wolfram.com/CyclicGroup.html
mathworld.wolfram.com/CyclicGroup.html
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The cyclic group C_9 is one of the two Abelian groups of group order 9 ... No modulo multiplication group is isomorphic to C_9 . Like all cyclic groups, C_9 ...
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mathworld.wolfram.com/CyclicGroupC9.html
mathworld.wolfram.com/CyclicGroupC9.html
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A cyclic group is a group in which there is an element x such that each element of the group may be written as for some integer k. In additive notation, this translates to . We say that x is a generator of the cyclic group or that the group is generated by x. ... ; Next: SUBGROUPS Up: Groups Previous: Order of a group...
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www.math.csusb.edu/notes/advanced/algebra/gp/node4.html
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4) = A Groups that can be generated in their entirety from one member are called cyclic groups. ... A few facts about cyclic groups and cyclic subgroups: ... Cyclic groups are Abelian.
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www.marlboro.edu/~mahoney/groups/dog_school/cyclic.html
www.marlboro.edu/~mahoney/groups/dog_school/cyclic.html
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Note that the isomorphisms mentioned in the previous paragraph imply that all cyclic groups of the same order are isomorphic to one another.
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planetmath.org/encyclopedia/CyclicGroup.html
planetmath.org/encyclopedia/CyclicGroup.html
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