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Hans Lausch 《Israel Journal of Mathematics》1984,47(1):29-31
It is shown that in an arbitrary finite groupG, any two maximal nilpotent subgroups ofG whose intersection contains its own centralizer inG, are conjugate inG. 相似文献
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We show that E8(2) has a unique conjugacy class of subgroups isomorphic to PSp4(5) and a unique conjugacy class of subgroups isomorphic to PSL3(5). There normalizers are maximal subgroups of E8(2) and are, respectively, isomorphic to PGSp4(5) and Aut(PSL3(5)). 相似文献
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We completely determine the conjugacy classes of maximal subgroups of the finite simple group F4(2) of Lie type, and of its automorphism group. 相似文献
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The goals of this paper are twofold. One is to look at the behavior of the collections of permutable subgroups and S-permutable
subgroups under the intersection map into a fixed subgroup of a group. The other is to locally analyze the intersection map
in connection with -, -, and -groups. In particular, we generalize Theorem 1 of Bauman [Arch. Math. (Basel) 25:337–340, 1974] to - and -groups.
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R. Fallah-Moghaddam 《代数通讯》2017,45(9):3724-3729
Let D be a noncommutative finite dimensional F-central division algebra and M a noncommutative maximal subgroup of GLn(D). It is shown that either M contains a noncyclic free subgroup or M is absolutely irreducible and there exists a unique maximal subfield K of Mn(D) such that K*M, K∕F is Galois with Gal(K∕F)?M∕K* and Gal(K∕F) is a finite simple group. 相似文献
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J. D. Key 《Geometriae Dedicata》1975,4(2-4):377-386
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Angel Cano 《Bulletin of the Brazilian Mathematical Society》2008,39(4):573-586
In this paper we look at a special type of discrete subgroups of PSL
n+1(C) called Schottky groups. We develop some basic properties of these groups and their limit set when n > 1, and we prove that Schottky groups only occur in odd dimensions, i.e., they cannot be realized as subgroups of PSL
2n+1(C).
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Let n be a positive integer. In this paper, using the results on the existence of primitive divisors of Lucas numbers and some properties of quadratic and exponential diophantine equations, we prove that if n ≡ 3 (mod 6), then the equation x 2 + (3n 2 + 1) y = (4n 2 + 1) z has only the positive integer solutions (x, y, z) = (n, 1, 1) and (8n 3 + 3n, 1, 3). 相似文献
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Simon M. Goodwin 《Transformation Groups》2006,11(1):51-76
Let G be a simple algebraic group over the algebraically closed field k of characteristic p ≥ 0. Assume p is zero or good
for G. Let B be a Borel subgroup of G; we write U for the unipotent radical of B and u for the Lie algebra of U. Using relative
Springer isomorphisms} we analyze the adjoint orbits of U in u. In particular, we show that an adjoint orbit of U in u contains
a unique so-called minimal representative. In case p > 0, assume G is defined and split over the finite field of p elements
Fp. Let q be a power of p and let G(q) be the finite group of Fq-rational points of G. Let F be the Frobenius morphism such that G(q) = GF. Assume B is F-stable, so that U is also F-stable and U(q) is a Sylow p-subgroup of G(q). We show that the conjugacy classes
of U(q) are in correspondence with the F-stable adjoint orbits of U in u. This allows us to deduce results about the conjugacy
classes of U(q). 相似文献
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