1986, N. S. Gopalakrishnan, University Algebra, New Age International, 2nd Edition, page 22, Proposition 1.5.6. Any subgroup of an infinite cyclic group is also an infinite cyclic group.
Source: wiktionary
Cyclic group
Synonyms for "cyclic group" (12 found)
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OpenGloss and ConceptNet supply richer edges like generalizations, collocations, and derivations.
More general
6 entriesMore specific
7 entriesbenzene ringcell cyclecyclohexane ringfinite cyclic groupinfinite cyclic grouplife cycleseasonal cycle
Collocations
12 entriescyclic behaviorcyclic group structurecyclic growthcyclic patterncyclic processcyclic schedulecyclic subgroupcyclic trendfinite cyclic groupgroup generatorgroup orderinfinite cyclic group
Inflections
3 entriescyclic groupsmore cyclicmost cyclic
Derivations
2 entriesSample sentences
3 total sentences available.
If u#58;G#95;1#92;rightarrow#92;mathbb#123;Z#125;#47;m#92;mathbb#123;Z#125; and v#58;G#95;2#92;rightarrow#92;mathbb#123;Z#125;#47;m#92;mathbb#123;Z#125; are isomorphisms of two cyclic groups with #92;mathbb#123;Z#125;#47;m#92;mathbb#123;Z#125;, then v#123;-1#125;#92;circu#58;G#95;1#92;rightarrowG#95;2 is an isomorphism.
Source: wiktionary
2003, Alexander Retakh (translator), Ėrnest Borisovich Vinberg, A Course in Algebra, [2001, Э. Б. Винберг, Курс алгебры, Factorial Press] American Mathematical Society, page 152, Cyclic groups are the simplest groups imaginable.
Source: wiktionary