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1.
In the present paper we give necessary and sufficient conditions for the subgroup separability of the fundamental group of a finite graph of groups with finitely generated abelian vertex groups.
2.
We give a characterization of the cyclic subgroup separability and weak potency of the fundamental group of a graph of polycyclic-by-finite groups and free-by-finite groups amalgamating edge subgroups of the form × D,where h has infinite order and D is finite. 相似文献
3.
Daniel T. Wise 《Geometriae Dedicata》2002,94(1):215-223
We construct an example of a finitely generated
group G such that rank((G
)n)=2 for all n1. For each n, we construct a finitely presented
group G
n
such that rank((G
n
)n)=2. We conjecture that if G is a word-hyperbolic group then rank(G
n
) as $ n. For each m we give an example of a residually finite
group K
m
such that K
m
has exactly two relators, but K
m
has no proper subgroups of index $ m. We construct a finitely generated
group D such that there is an epimorphism DD×D. 相似文献
4.
We prove that if a group G is residually
, then for every
-subgroup of the group G, the set of -roots from this subgroup is a -separable
-subgroup. 相似文献
5.
Let R be a homogeneous ring over an infinite field, IR a homogeneous ideal, and
I an ideal generated by s forms of degrees d
1,...,d
s
so that codim(
:I)s. We give broad conditions for when the Hilbert function of R/
or of R/(
:I) is determined by I and the degrees d
1,...,d
s
. These conditions are expressed in terms of residual intersections of I, culminating in the notion of residually S
2 ideals. We prove that the residually S
2 property is implied by the vanishing of certain Ext modules and deduce that generic projections tend to produce ideals with this property. 相似文献
6.
7.
设H是有限生成的无挠幂零群G的一个子群,如果H满足条件:对G的任意元素g及任意自然数n,从gn∈H可以推出g∈H,那么当素数p充分大时,∩∞i=1HGpi=H。 相似文献
8.
In Oman and Salminen [19], the authors introduce and study residually small rings, defined as follows: an infinite commutative ring R with identity is residually smallif for every r∈R?{0}, there exists an ideal Ir of R such that r?Ir and |R∕Ir|<|R|. The purpose of this note is to extend our study. In particular, we continue our investigation of residually small rings and then generalize this notion to modules. 相似文献
9.
设幂零群G=KP=PK,其中P是有限秩的幂零p-群,K是G的有限秩的p-自由的正规子群,p不属于K的谱Sp(K).设1=ζ0Gζ1G···ζcG=G是G的上中心列,α和β是G的两个p-自同构,把α,β在每个ζiG/ζi-1G上的诱导自同构分别记为αi和βi,又记Ii:=Im(αiβi-βiαi),则(i)如果每个Ii都是有限循环群,并且I:=(αβ(g))(βα(g))-1|g∈G是G的有限子群,那么α和β生成一个有限p-群;(ii)如果Ii或为有限循环群,或为拟循环p-群,或为Zpn⊕Zp∞对某自然数n,那么α和β生成一个可解的剩余有限p-群,它是有限生成的无挠幂零群被有限p-群的扩张;(iii)如果Ii或为有限循环群,或为拟循环p-群,或为Zpn⊕Zp∞,或为无挠的局部幂零群,或Ii有正规列1JiIi,其商因子分别为有限循环群、无挠的局部幂零群,或Ii=Zp∞⊕Ji,Ji为无挠的局部幂零群,或Ii有正规列1KiJiIi,其商因子分别为有限循环群、拟循环p-群、无挠的局部循环群,那么α和β生成一个可解的剩余有限p-群,它的幂零长度至多是3.特别地,当K是一个FC-群时,在情形(iii),α和β生成的群也是有限生成的无挠幂零群被有限p-群的扩张.此外,如果G=KP里,K是一个FC-群,对G的下中心列考虑了类似的问题,得到了"对偶"的结果. 相似文献
10.
Benjamin Fine Olga G. Kharlampovich Alexei G. Myasnikov Vladimir N. Remeslennikov G. Rosenberger 《代数通讯》2013,41(8):3386-3394
We prove that the automorphism group of a finitely generated fully residually free group is tame. 相似文献