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The order of the product of two elements

Author

Listed:
  • Xianhua Li

    (Soochow University)

  • Donglin Lei

    (Soochow University)

  • Yaxin Gao

    (Soochow University)

Abstract

We prove that in a finite group G, $$|ab|=|a||b|$$ | a b | = | a | | b | if and only if $$ab=ba$$ a b = b a for all elements a, b of G whose orders are factor of the m-th power of different primes, where m is a given integer.

Suggested Citation

  • Xianhua Li & Donglin Lei & Yaxin Gao, 2022. "The order of the product of two elements," Indian Journal of Pure and Applied Mathematics, Springer, vol. 53(2), pages 372-374, June.
    • Handle: RePEc:spr:indpam:v:53:y:2022:i:2:d:10.1007_s13226-021-00007-w
    DOI: 10.1007/s13226-021-00007-w
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    Cited by:

    1. Fontes, Dalila B.M.M. & Homayouni, S. Mahdi & Gonçalves, José F., 2023. "A hybrid particle swarm optimization and simulated annealing algorithm for the job shop scheduling problem with transport resources," European Journal of Operational Research, Elsevier, vol. 306(3), pages 1140-1157.
    2. Luiz Morais-da-Silva, Rodrigo & Glufke Reis, Germano & Sanctorum, Hermes & Forte Maiolino Molento, Carla, 2022. "The social impacts of a transition from conventional to cultivated and plant-based meats: Evidence from Brazil," Food Policy, Elsevier, vol. 111(C).
    3. Ali, Haider & Siddiqui, Muhammad Usama & Ammar, & Aswani, Muhammad Ahsan & Umer, Muhammad & Khan, Muhammad Ismail, 2024. "Techno-economic analysis of various configurations of stand-alone PV-RO systems for Pakistan," Renewable Energy, Elsevier, vol. 225(C).

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