Finite Groups with All Maximal Subgroups of Prime or Prime Square Index
1964 ◽
Vol 16
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pp. 435-442
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In this paper finite groups with the property M, that every maximal subgroup has prime or prime square index, are investigated. A short but ingenious argument was given by P. Hall which showed that such groups are solvable.B. Huppert showed that a finite group with the property M, that every maximal subgroup has prime index, is supersolvable, i.e. the chief factors are of prime order. We prove here, as a corollary of a more precise result, that if G has property M and is of odd order, then the chief factors of G are of prime or prime square order. The even-order case is different. For every odd prime p and positive integer m we shall construct a group of order 2apb with property M which has a chief factor of order larger than m.
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2012 ◽
Vol 49
(3)
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pp. 390-405
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1970 ◽
Vol 3
(2)
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pp. 273-276
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2014 ◽
Vol 57
(3)
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pp. 648-657
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2017 ◽
Vol 16
(11)
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pp. 1750217
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2009 ◽
Vol 08
(02)
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pp. 229-242
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2019 ◽
Vol 18
(05)
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pp. 1950087
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