A studying about some characterization of finite matroid groups (Journal of Sciences & Technology, 2020)
In this work, we show that a very large class of matroid groups possesses the basis property. Moreover, we show that this class behaves like vector spaces in terms of basis. Applications include new proofs for the characterization of finite matroid groups. Moreover, we show that every group possesses BEP, also possesses the span property and in the deﬁnition of matroid group, the extension property can be replaced by BEP. The fact that BEP always correct in vector spaces, but the situation is diﬀerent in groups was showed. In the end, we show that each base and maximal independent subset are equivalent in any group with embedding property.