Z.Bao, Maximum order of finite abelian subgroups in the outer automorphism group of a rank n free group. J. Algebra 236, 355-370 (2001)Z. Bao, Maximum order of finite abelian subgroups in the outer au- tomorphism group of a rank n free group, J. Algebra 236 (2001), 355-370....
Suppose that GG is a finite abelian group and that x,y∈Gx,y∈G are of orders aa and bb respectively. I'm trying to show that there exist two elements x′x′ and y′y′ of orders a′a′ and b′b′ such that a′b′=lcm(a,b)a′b′=lcm(a,b) and gcd(a′,b′)=1...
A group of generalized finitary automorphisms of an abelian group We study the groupIAut(A)${\\operatorname{IAut}(A)}$generated by the inertial automorphisms of an abelian groupA, that is, automorphismsγ${{\\gamma}}$with the property that each subgroupHofAhas finite index in the subg...
A unital $\ell$-group $(G,u)$ is an abelian group $G$ equipped with atranslation-invariant lattice-order and a distinguished element $u$, calledorder-unit, whose positive integer multiples eventually dominate each elementof $G$. We classify finitely generated unital $\ell$-groups by sequenc...
We compute the order of the unitary subgroup of the group of units when G is either an extraspecial 2-group or the central product of such a group with a cyclic group of order 4 or G has an abelian subgroup A of index 2 and an element b such that b inverts each element of A. ...
说备Let G be an Abelian group of order 30. Then Aut(H) is ( ).说备A non-Abelian说备B cyclic
We establish an asymptotic formula for the Dirichlet summatory function of ^& , up to an order term which is best possible on the basis of the present knowledge about the zeros of the Riemann zeta-function.关键词: counting function abelian group semisimple group dirichlet series asymptotic ...
Let o(G) be the average order of a finite group G. We show that if o(G)<c, where c∈{136,114}, then G is an elementary abelian 2-group or a solvable group, respectively. Also, we prove that the set containing the average orders of all finite groups is not dense in [a,∞)...
Showing a limited preview of this publication: Appendix 57p-groups with a 2-uniserial subgroupof orderpand an abelian subgroup oftype(p,p)LetLbe a proper subgroup of ap-groupGand letC(L,G)be the number of maximalchains connectingLwithG(a chainL=L0<L1<⋅⋅⋅<Ln=Gis said to be...
Finally we show that, in contrast to the fact that all theories of totally ordered Abelian groups have the same universal part, there are uncountably many universal theories of Abelian cyclically ordered groups. 展开 关键词: Cyclically ordered groups First-order theory Orderable Universal theory ...