What are the fundamental concepts of group theory?

@article{Burn1996WhatAT,
  title={What are the fundamental concepts of group theory?},
  author={Bob Burn},
  journal={Educational Studies in Mathematics},
  year={1996},
  volume={31},
  pages={371-377}
}
This paper offers a critical analysis of Dubinsky et al. (1994) and proposes, as an alternative to the four axioms and the standard definitions, that permutation and symmetry may be regarded as the fundamental concepts of group theory. 

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