@article{Suksumran2023, 
author = {Teerapong Suksumran},
title = {Two theorems on direct products of gyrogroups},
year = {2023},
journal = {AIMS Mathematics},
volume = {8},
number = {3},
pages = {6278-6287},
keywords = {gyrogroup, homomorphism, direct product theorem, cancellation theorem, decomposition of gyrogroup},
url = {https://www.sciopen.com/article/10.3934/math.2023317},
doi = {10.3934/math.2023317},
abstract = {We extend two standard theorems on groups to gyrogroups: the direct product theorem and the cancellation theorem for direct products. Firstly, we prove that under a certain condition a gyrogroup    G can be decomposed as the direct product of two subgyrogroups. Secondly, we prove that finite gyrogroups can be cancelled in direct products: if    A  ≅  B, then    A  ×  H  ≅  B  ×  K or    H  ×  A  ≅  K  ×  B implies    H  ≅  K, where    A  ,  B  ,  H  , and    K are finite gyrogroups.}
}