Class-preserving coleman automorphisms of permutational wreath products with 2-closed base groups
2016 ◽
Vol 15
(10)
◽
pp. 1650189
Keyword(s):
Let [Formula: see text] be a nontrivial [Formula: see text]-closed group and let [Formula: see text] be an arbitrary permutation group on a finite set [Formula: see text]. Let [Formula: see text] be the corresponding permutational wreath product of [Formula: see text] by [Formula: see text]. It is shown that every class-preserving Coleman automorphism of [Formula: see text]-power order of [Formula: see text] is inner. As a direct consequence, it is obtained that the normalizer property holds for [Formula: see text]. Further, it is shown that every class-preserving Coleman automorphism of [Formula: see text] is inner whenever [Formula: see text] is nilpotent. Our results generalize some known ones.
2014 ◽
Vol 13
(05)
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pp. 1350156
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2012 ◽
Vol 92
(1)
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pp. 127-136
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1989 ◽
Vol 40
(2)
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pp. 255-279
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2002 ◽
Vol 65
(2)
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pp. 277-288
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2012 ◽
Vol 55
(2)
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pp. 390-399
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1982 ◽
Vol 33
(1)
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pp. 76-85
Keyword(s):
Keyword(s):
2015 ◽
Vol 26
(01)
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pp. 1550003
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