FINITE GROUPS WITH SOME NON-CYCLIC SUBGROUPS HAVING SMALL INDICES IN THEIR NORMALIZERS
2014 ◽
Vol 13
(04)
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pp. 1350141
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In this paper, it is shown that a finite group G is always supersolvable if |NG(H) : H| ≤ 2 for every non-cyclic subgroup H of G of prime-power order. Also, finite groups with all supersolvable non-cyclic subgroups being self-normalizing, and finite p-groups with all non-cyclic proper subgroups being of prime index in their normalizers are completely classified.
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1986 ◽
Vol 40
(2)
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pp. 253-260
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1982 ◽
Vol 25
(1)
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pp. 19-20
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2013 ◽
Vol 13
(02)
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pp. 1350100
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1977 ◽
Vol 20
(3)
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pp. 229-232
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2010 ◽
Vol 82
(2)
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pp. 293-304
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2015 ◽
Vol 14
(06)
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pp. 1550095
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