, By Remark 1 after the statement of Theorem 7.2, it suffices to treat the case when G is RTFN
,
, Assume the contrary, then since Z/pZ[G] is a skew field, there exists L = (? 1 | · · · |? n ) ? M 1,n ( Z/pZ[G]) \ {0} such that LA = 0. By Corollary 10.3, for N large enough the imageL ? Z/pZ[G/G N ] is well-defined, and we haveL? = 0, where? is the image of A in M n
, On the other hand, since G/G N is nilpotent, A fortiori it is not invertible in M n
, Again by Corollary 10.3, B has a well-defined imageB ? M n ( Z/pZ, and?B = I n =B?. ThusB is the inverse of? ? M n, vol.18, pp.1045-1087, 2013.
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