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2.
3.
R. J. Zimmer 《Inventiones Mathematicae》1984,75(3):425-436
4.
Let be a group generated by a finite set S. We give a sufficient
condition for to have Kazhdan's property (T). This condition is
easy to check and gives Kazhdan constants. We give examples of
groups to which this method applies. We prove that in some setting
generic presentations define groups which satisfy this condition and
thus have property (T). Moreover we prove that small changes in the
presentation of a group satisfying this condition do not change the
fact that the group has property (T). 相似文献
5.
Yingjue Fang 《Journal of Number Theory》2011,131(11):2078-2080
Let E be a finite dimensional symplectic space over a local field of characteristic zero. We show that for every element in the metaplectic double cover of the symplectic group Sp(E), and are conjugate by an element of GSp(E) with similitude −1. 相似文献
6.
Carlo Casolo 《manuscripta mathematica》1994,82(1):171-189
We study finite groups G in which the number of distinct prime divisors of the length of the conjugacy classes is at most
three. In particular we prove, under this condition, a conjecture of B. Huppert on the number of prime divisors of ÷G/Z(G)÷. 相似文献
7.
V. Roman’kov 《Journal of Pure and Applied Algebra》2011,215(4):664-671
Let N be a finitely generated nilpotent group. We show that there is an algorithm that for any automorphism φ∈Aut(N) computes its Reidemeister number R(φ). It is proved that any free nilpotent group Nrc of rank r and class c belongs to class R∞ if any of the following conditions holds: r=2 and c≥4; r=3 and c≥12; r≥4 and c≥2r. 相似文献
8.
Lucia Morotti 《代数通讯》2018,46(3):1066-1079
A conjugacy class C of a finite group G is a sign conjugacy class if every irreducible character of G takes value 0,1 or ?1 on C. In this paper, we classify the sign conjugacy classes of alternating groups. 相似文献
9.
Avinoam Mann 《Israel Journal of Mathematics》1990,71(1):55-63
We derive some properties of a family of finite groups, which was investigated by Camina, Macdonald, and others. For instance,
we give information about the Schur multipliers of the class twop-groups in this family.
A large part of this paper was written while the author was visiting the Department of Mathematics of the University of Trento.
The author is indebted to this department, and in particular to C.M. Scoppola, for their kind hospitality. The author is also
grateful to D. Chillag for his constructively destructive criticism of the first version of this paper. 相似文献
10.
Dan Rossi 《Archiv der Mathematik》2018,110(2):99-108
We show that if a finite group G has exactly three rational conjugacy classes, then G also has exactly three rational-valued irreducible complex characters. This generalizes a result of Navarro and Tiep (Trans Amer Math Soc 360:2443–2465, 2008) and partially answers in the affirmative a conjecture of theirs. We also give a family of examples of non-solvable groups with exactly three rational conjugacy classes. 相似文献
11.
We classify all finite groupsG such that the product of any two non-inverse conjugacy classes ofG is always a conjugacy class ofG. We also classify all finite groupsG for which the product of any twoG-conjugacy classes which are not inverse modulo the center ofG is again a conjugacy class ofG. 相似文献
12.
George Lusztig 《Transformation Groups》1996,1(1-2):83-97
We define a map from an affine Weyl group to the set of conjugacy classes of an ordinary Weyl group.
Supported in part by the National Science Foundation. 相似文献
13.
Thomas Michael Keller 《Israel Journal of Mathematics》2011,181(1):433-444
In his paper Finite groups have many conjugacy classes (J. London Math. Soc (2) 46 (1992), 239–249), L. Pyber proved the to-date best general lower bounds for the number of conjugacy classes of a finite group
in terms of the order of the group. In this paper we strengthen the main results in Pyber’s paper. 相似文献
14.
Let G be a finite group and let x G denote the conjugacy class of an element x of G. We classify all finite groups G in the following three cases: (i) Each non-trivial conjugacy class of G together with the identity element 1 is a subgroup of G, (ii) union of any two distinct non-trivial conjugacy classes of G together with 1 is a subgroup of G, and (iii) union of any three distinct non-trivial conjugacy classes of G together with 1 is a subgroup of G. 相似文献
15.
Let
be a (not necessarily semi-finite) σ-finite von Neumann algebra. We prove that there exists a finite von Neumann algebra
so that for every 1 < p < 2, the Haagerup L
p
-space associated with
embeds isomorphically into
. We also provide a proof of the following non-commutative generalization of a classical result of Rosenthal: if
is a semi-finite von Neumann algebra then every reflexive subspace of
embeds isomorphically into L
r
(
) for some r > 1.
Dedicated to Professor H. P. Rosenthal on the occasion of his sixty-fifth birthday
Research partially supported by NSF grant DMS-0456781. 相似文献
16.
17.
A finite group G is called an ah-group if any two distinct conjugacy classes of G have distinct cardinality. We show that if G is an ah-group, then the non-abelian socle of G is isomorphic to one of the following:
- 1. , for 1a5, a≠2.
- 2. A8.
- 3. PSL(3,4)e, for 1e10.
- 4. A5×PSL(3,4)e, for 1e10.
- 1. , for 3a5.
- 2. PSL(3,4)e, for 1e10.
18.
Guy Alfandary 《Israel Journal of Mathematics》1994,86(1-3):211-220
LetG be a finite group. Attach toG the following two graphs: Γ — its vertices are the non-central conjugacy classes ofG, and two vertices are connected if their sizes arenot coprime, and Γ* — its vertices are the prime divisors of sizes of conjugacy classes ofG, and two vertices are connected if they both divide the size of some conjugacy class ofG. We prove that whenever Γ* is connected then its diameter is at most 3, (this result was independently proved in [3], for
solvable groups) and Γ* is disconnected if and only ifG is quasi-Frobenius with abelian kernel and complements. Using the method of that proof we give an alternative proof to Theorems
in [1],[2],[6], namely that the diameter of Γ is also at most 3, whenever the graph is connected, and that Γ is disconnected
if and only ifG is quasi-Frobenius with abelian kernel and complements. As a result we conclude that both Γ and Γ* have at most two connected
components. In [2],[3] it is shown that the above bounds are best possible.
The content of this paper corresponds to a part of the author’s Ph.D. thesis carried out at the Tel Aviv University under
the supervision of Prof. Marcel Herzog. 相似文献
19.
For a wide class of saturated weakly branch groups, including the (first) Grigorchuk group and the Gupta-Sidki group, we prove
that the Reidemeister number of any automorphism is infinite.
相似文献
20.
Robert M. Guralnick 《Proceedings of the American Mathematical Society》2007,135(3):689-693
We show that if is a reductive group, then th roots of conjugacy classes are a finite union of conjugacy classes, and that if is an algebraic overgroup of , then the intersection of with a conjugacy class of is a finite union of -conjugacy classes. These results follow from results on finiteness of unipotent classes in an almost simple algebraic group.