= Nakayama block theorem
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= Nakayama Conjecture for symmetric groups
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{synonym}
At fixed degree $n$ in positive <characteristic> $p$, two <Specht modules> belong to the same <block of a group algebra> exactly when their labels have the same <core of a partition> at modulus $p$. The simple labels in that block are precisely the <regular partitions> with that core. The theorem follows by combining the <residue-content criterion for symmetric-group blocks> with the <Jucys–Murphy description of the center of a symmetric-group algebra>.
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