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Relations between some axiom systems for matroids and the automorphism groups of a matroid

MAO Hua,LIU San yang (School of Science, Xidian Univ., Xi′an 710071, China)  
This paper discusses the relations between five axiom systems for matroids and the automorphism groups of a matroid. The five axiom systems are independent axioms, base axioms, rank axioms, hyperplane axioms, and closure axioms. The result is that for the automorphism groups of a matroid, there are only independent axioms, base axioms and rank axioms, but no hyperplane axioms and closure axioms. The aim of the discussion is to apply suitable axioms to different problems so that every problem will be solved easily.
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