new classes of infinite groups
نویسندگان
چکیده
in this article, we consider some new classes of groups, namely, mp-groups, t0-groups,ø-groups,ø0-groups, groups with finitely embedded involution, which were appeared at the end of twenties century. these classes of infinite groups with finiteness conditions were introduced by v.p. shunkov. we give some review of new results on these classes of groups.
منابع مشابه
On Minimal Fitting Classes of Periodic, Infinite Groups
Examples of Fitting classes generated by certain periodic infinite groups are presented in this paper. The groups in question are finite extensions of direct products of quasi-cyclic (Priifer) groups and are, in particular, Cernikov groups. The methods applied follow closely those used for constructing Fitting classes of finite groups, especially in the case of nilpotent length three. 1991 Math...
متن کاملgroups whose proper subgroups of infinite rank have polycyclic-by-finite conjugacy classes
a group g is said to be a (pf)c-group or to have polycyclic-by-finite conjugacy classes, if g/c_{g}(x^{g}) is a polycyclic-by-finite group for all xin g. this is a generalization of the familiar property of being an fc-group. de falco et al. (respectively, de giovanni and trombetti) studied groups whose proper subgroups of infinite rank have finite (respectively, polycyclic) conjugacy classes. ...
متن کاملNew infinite classes of 1-factorizations of complete graphs
Some classes of I-factorizations of complete graphs are known. They are GK2n , AK2n , W K 2n and their variations, and automorphism-free I-factorizations. In this paper, for any positive integer t, we construct new I-factorizations NtK 2n which are defined for all 2n with 2n ~ 6t. They also have some variations.
متن کاملThe graph of equivalence classes and Isoclinism of groups
Let $G$ be a non-abelian group and let $Gamma(G)$ be the non-commuting graph of $G$. In this paper we define an equivalence relation $sim$ on the set of $V(Gamma(G))=Gsetminus Z(G)$ by taking $xsim y$ if and only if $N(x)=N(y)$, where $ N(x)={uin G | x textrm{ and } u textrm{ are adjacent in }Gamma(G)}$ is the open neighborhood of $x$ in $Gamma(G)$. We introduce a new graph determined ...
متن کاملInfinite Groups
Most interesting groups arise as a group of transformations. For example the set of “rigid motions” of 2-dimensional space R forms a group denoted Isom(R). There are three kinds of transformations: reflection about a line, rotation about a point, and translation in a direction. These form a group under composition (i.e., do one transformation and then do the other). For example, the composition...
متن کاملSome numerical results on two classes of finite groups
In this paper, we consider the finitely presented groups $G_{m}$ and $K(s,l)$ as follows;$$G_{m}=langle a,b| a^m=b^m=1,~[a,b]^a=[a,b],~[a,b]^b=[a,b]rangle $$$$K(s,l)=langle a,b|ab^s=b^la,~ba^s=a^lbrangle;$$and find the $n^{th}$-commutativity degree for each of them. Also we study the concept of $n$-abelianity on these groups, where $m,n,s$ and $l$ are positive integers, $m,ngeq 2$ and $g.c.d(s,...
متن کاملمنابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
iranian journal of numerical analysis and optimizationجلد ۱، شماره ۱، صفحات ۰-۰
میزبانی شده توسط پلتفرم ابری doprax.com
copyright © 2015-2023