ABSTRACT. Recentlythe first two authors have introduced a group invariant,called exterior degree, which is related to the number of elements x and y of a finitegroup Gsuchthat x∧y=1 inthe exteriorsquareG∧Gof G. Researchon thistopic gives somerelationsbetweenthisconcept,theSchur multiplierand the capability of a finite group. In the present paper, we will generalize the concept of exterior degree of groups and we will introduce the multiple exterior degree of finite groups. Among other results, we willobtain some relations between the multiple exterior degree, multiple commutativity degree and capability of finite groups.

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