Abstract
A characterization of a finite p p -solvable group G G with t ( G ) > ( r + 2 ) ( p − 1 ) + 1 t(G) > (r + 2)(p - 1) + 1 is given under certain conditions, where t ( G ) t(G) is the nilpotency index of the radical of a group algebra of a finite p p -solvable group G G with a p p -Sylow subgroup of order p r {p^r} over a field of characteristic p p .
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