共查询到20条相似文献,搜索用时 15 毫秒
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D. O. Revin 《Algebra and Logic》2008,47(3):210-227
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We prove that ifA≠1 is a subgroup of a finite groupG and the order of an element in the centralizer ofA inG is strictly larger (larger or equal) than the index [G:A], thenA contains a non-trivial characteristic (normal) subgroup ofG. Consequently, ifA is a stabilizer in a transitive permutation group of degreem>1, thenexp(Z(A))<m. These theorems generalize some recent results of Isaacs and the authors. 相似文献
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Monomial characters and normal subgroups 总被引:3,自引:0,他引:3
Everett C. Dade 《Mathematische Zeitschrift》1981,178(3):401-420
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Andrea Lucchini 《Archiv der Mathematik》1995,64(4):273-276
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I. Martin Isaacs 《Mathematische Zeitschrift》1983,182(2):205-221
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In this paper we study the family of finite groups with the property that every maximal abelian normal subgroup is self-centralizing. It is well known that this family contains all finite supersolvable groups, but it also contains many other groups. In fact, every finite group G is a subgroup of some member \(\Gamma \) of this family, and we show that if G is solvable, then \(\Gamma \) can be chosen so that every abelian normal subgroup of G is contained in some self-centralizing abelian normal subgroup of \(\Gamma \). 相似文献
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Groups with maximal subgroups of Sylow subgroups normal 总被引:3,自引:0,他引:3
Gary L. Walls 《Israel Journal of Mathematics》1982,43(2):166-168
This paper characterizes those finite groups with the property that maximal subgroups of Sylow subgroups are normal. They
are all certain extensions of nilpotent groups by cyclic groups. 相似文献
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I. M. Isaacs 《Transactions of the American Mathematical Society》2004,356(3):1155-1183
We consider the degrees of those irreducible characters of a group whose kernels do not contain a given normal subgroup . We show that if and is not perfect, then the common-divisor graph on this set of integers has at most two connected components. Also, if is solvable, we obtain bounds on the diameters of the components of this graph and, in the disconnected case, we study the structure of and of .
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Avino’am Mann 《Israel Journal of Mathematics》1968,6(1):13-25
A group is said to have dense normal subgroups, if each non-empty open interval in its lattice of subgroups contains a normal
subgroup. The structure of this and related classes of groups is investigated. Typical results are: an infinite group with
dense ascendant subgroups is locally nilpotent: a nontorsion group with dense normal subgroups is abelian, etc. 相似文献
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B. Wilkens 《Israel Journal of Mathematics》2009,172(1):357-369
Let P be a finite p-group, p a prime. We prove that there is a finite p-group Q ≥ P such that every normal subgroup of Q is characteristic in Q. 相似文献
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Geometriae Dedicata - We examine distortion of finitely generated normal subgroups. We show a connection between subgroup distortion and group divergence. We suggest a method computing the... 相似文献
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In this note, we show that if
is a π-partial character of the π-separable group
is a chain of normal subgroups of G, and H is a Hall π-subgroup of G, then
has a Fong character α
Irr(H) such that for every subgroup
, every irreducible constituent of α
H∩N
is Fong for N. We also show that if
is quasi-primitive, then for every normal subgroup M of G the irreducible constituents of
are Fong for M.
Received: 21 July 2006 Revised: 17 January 2007 相似文献