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On Group-like Properties of Left Groups

Author

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  • Aftab Hussain Shah

    (Department of Mathematics, Central University of Kashmir, Ganderbal 191201, Jammu and Kashmir, India)

  • Bana Al Subaiei

    (Department of Mathematics and Statistics, College of Science, King Faisal University, P.O. Box 400, Al-Ahsa 31982, Saudi Arabia)

  • Shariq Ali Attari

    (Department of Mathematics, Central University of Kashmir, Ganderbal 191201, Jammu and Kashmir, India)

  • Dilawar Juneed Mir

    (Department of Mathematics, University Institute Sciences, Chandigarh University, Mohali 140413, Punjab, India)

Abstract

A left group is a semigroup that is the direct product of a left zero semigroup and a group. In this paper, we investigate some group-like properties of left groups. In particular, we characterise monogenic left group monoids and prove some fundamental results on left group morphisms. We also characterise Green’s equivalences on left groups and, analogously to groups, establish a correspondence between congruences and normal sub-left groups. Finally, we characterise DSC left groups.

Suggested Citation

  • Aftab Hussain Shah & Bana Al Subaiei & Shariq Ali Attari & Dilawar Juneed Mir, 2025. "On Group-like Properties of Left Groups," Mathematics, MDPI, vol. 13(19), pages 1-16, September.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:19:p:3109-:d:1760442
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