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201.
Martin R. Bridson 《Journal of the American Mathematical Society》1999,12(4):1103-1118
It is shown that there exist infinitely many non-integers such that the Dehn function of some finitely presented group is . Explicit examples of such groups are constructed. For each rational number pairs of finitely presented groups are constructed so that the distortion of in is .
202.
Jürgen?EckerEmail author 《Abhandlungen aus dem Mathematischen Seminar der Universit?t Hamburg》2003,73(1):229-239
We show that compatible functions can be lifted from quotients modulo distributive minimal normal subgroups. This enables
us to describe the 1-affine complete groups with a distributive minimal normal subgroup. As an application, we characterise
thek-affine complete finite Frobenius groups for everyk ∈ N. 相似文献
203.
A. M. Protopopov 《Algebra and Logic》2003,42(4):279-286
We study into the question of whether a partial order can be induced from a partially right-ordered group
onto a space
of right cosets of
w.r.t. some subgroup
of
. Examples are constructed showing that the condition of being convex for
in
is insufficient for this. A necessary and sufficient condition (in terms of a subgroup
and a positive cone
of
) is specified under which an order of
can be induced onto
. Sufficient conditions are also given. We establish properties of the class of partially right-ordered groups
for which
is partially ordered for every convex subgroup
, and properties of the class of groups such that
is partially ordered for every partial right order
on
and every subgroup
that is convex under
. 相似文献
204.
Gerold Alsmeyer 《Journal of Theoretical Probability》2002,15(2):259-283
It is proved that for each random walk (S
n
)
n0 on
d
there exists a smallest measurable subgroup
of
d
, called minimal subgroup of (S
n
)
n0, such that P(S
n
)=1 for all n1.
can be defined as the set of all x
d
for which the difference of the time averages n
–1
n
k=1
P(S
k
) and n
–1
n
k=1
P(S
k
+x) converges to 0 in total variation norm as n. The related subgroup
* consisting of all x
d
for which lim
n P(S
n
)–P(S
n
+x)=0 is also considered and shown to be the minimal subgroup of the symmetrization of (S
n
)
n0. In the final section we consider quasi-invariance and admissible shifts of probability measures on
d
. The main result shows that, up to regular linear transformations, the only subgroups of
d
admitting a quasi-invariant measure are those of the form
1×...×
k
×
l–k
×{0}
d–l
, 0kld, with
1,...,
k
being countable subgroups of
. The proof is based on a result recently proved by Kharazishvili(3) which states no uncountable proper subgroup of
admits a quasi-invariant measure. 相似文献
205.
We prove a new formula about local control of the number of p-regular conjugacyclasses of a finite group. We then relate the results to Alperins weight conjecture to obtain newresults describing the number of simple modules for a finite group in terms of weights of solvablesubgroups. Finally, we use the results to obtain new formulations of Alperins weight conjecture,and to obtain restrictions on the structure of a minimal counterexample. 相似文献
206.
在本文中,我们构造了l-群簇的列B=B1■B……■Bn■Bn+1■…■BW。它推广了ConradP.(Symposia math 21(1977)的扭类B,其主要结果如下: (Ⅰ)BW∩FV=F Bn∩Fn■Bn+1∩FV (Ⅱ)设m是一个正整数,令B0=Φ,则G∈(Bm∩F)\(Bm=1∩FV)当且仅当G是O-群的小字典和且此和的厚度为m。 相似文献
207.
E. A. Gorin 《Mathematical Notes》2000,68(2):167-172
The existence of homeomorphisms establishign an isometry of normalized Haar measures on (metrizable) compact groups is studied.
In the case of 0-dimensional groups, a complete answer is given in terms of the indices of open normal subgroups. For example,
for the countable powers of the groups ℤ/(m) and ℤ/(n), the answer is affirmative if and only ifm andn have the same prime divisors. A certain class of extensions of 0-dimensional groups is also studied.
Translated fromMatematicheskie Zametki, Vol. 68, No. 2, pp. 188–194, August, 2000. 相似文献
208.
R. I. Grigorchuk 《Mathematical Notes》2000,67(6):718-723
The class of branch groups is defined (both in the abstract and in the profinite category). The relationship of this class
with the class of extremal groups is established. Properties of the branch groups are investigated. Applications of the congruence
property to the theory of profinite branch groups are indicated. The weak maximality of parabolic subgroups in branch groups
is proved.
Translated fromMatematicheskie Zametki, Vol. 67, No. 6, pp. 852–858, June, 2000. 相似文献
209.
210.