Solvable and Nilpotent Subgroups of GL(n,qm)
1982 ◽
Vol 34
(5)
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pp. 1097-1111
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Keyword(s):
Let V ≠ 0 be a vector space of dimension n over a finite field of order qm for a prime q. Of course, GL(n, qm) denotes the group of -linear transformations of V. With few exceptions, GL(n, qm) is non-solvable. How large can a solvable subgroup of GL(n, qm) be? The order of a Sylow-q-subgroup Q of GL(n, qm) is easily computed. But Q cannot act irreducibly nor completely reducibly on V.Suppose that G is a solvable, completely reducible subgroup of GL(n, qm). Huppert ([9], Satz 13, Satz 14) bounds the order of a Sylow-q-subgroup of G, and Dixon ([5], Corollary 1) improves Huppert's bound. Here, we show that |G| ≦ q3nm = |V|3. In fact, we show thatwhere
2017 ◽
Vol 103
(3)
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pp. 402-419
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1967 ◽
Vol 19
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pp. 281-290
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1961 ◽
Vol 13
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pp. 614-624
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1960 ◽
Vol 3
(2)
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pp. 143-148
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Keyword(s):
2019 ◽
Vol 19
(05)
◽
pp. 2050086
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Keyword(s):
2011 ◽
Vol 85
(1)
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pp. 19-25
1998 ◽
Vol 57
(1)
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pp. 59-71
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