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Cyclic Groups

In: Group Theory

Author

Listed:
  • Dinesh Khattar

    (University of Delhi, Department of Mathematics)

  • Neha Agrawal

    (University of Delhi, Department of Mathematics)

Abstract

In chapter one we established that the dihedral groups describe objects that have both rotational and bilateral symmetry, i.e., they look the same when flipped over in a specific direction, such as horizontally. The most basic family of groups, the cyclic groups, describe objects that have only rotational symmetry. Cyclic groups can be thought of as rotations, rotating an object a certain number of times till we eventually return to the original position. Cyclic groups have applications across a broad spectrum: in the fields of number theory, chaos theory, and cryptography, among others

Suggested Citation

  • Dinesh Khattar & Neha Agrawal, 2023. "Cyclic Groups," Springer Books, in: Group Theory, chapter 0, pages 99-118, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-21307-6_3
    DOI: 10.1007/978-3-031-21307-6_3
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