Geodesic
The Schur–Wielandt theory for central $S$-rings
Algebra i logika, Tome 55 (2016) no. 1, pp. 58-74

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Two basic results on $S$-rings over an Abelian group are the Schur theorem on multipliers and the Wielandt theorem on primitive $S$-rings over groups with a cyclic Sylow subgroup. Neither of these is directly generalized to the non-Abelian case. Nevertheless, we prove that the two theorems are true for central $S$-rings over any group, i.e., for $S$-rings that are contained in the center of the group ring of that group (such $S$-rings arise naturally in the supercharacter theory). Extending the concept of a $B$-group introduced by Wielandt, we show that every Camina group is a generalized $B$-group, whereas simple groups, with few exceptions, cannot be of this type.
Keywords: $S$-ring
Mots-clés : conjugacy class, $B$-group. 
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     author = {M. E. Muzychuk and I. N. Ponomarenko and G. Chen},
     title = {The {Schur{\textendash}Wielandt} theory for central $S$-rings},
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     pages = {58--74},
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     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2016_55_1_a3/}
}
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M. E. Muzychuk; I. N. Ponomarenko; G. Chen. The Schur–Wielandt theory for central $S$-rings. Algebra i logika, Tome 55 (2016) no. 1, pp. 58-74. http://geodesic.mathdoc.fr/item/AL_2016_55_1_a3/