Results 271 to 280 of about 7,164 (304)
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Journal of Group Theory, 2003
A group \(G\) is called \(R^*\)-group if for all \(n>0\) and elements \(g\) and \(x_1,\dots,x_n\) the equation \(g^{x_1 }\cdots g^{x_n }=1\) implies \(g=1\). The following results are proved: (1) if \(G\) is an Abelian-by-nilpotent as well as nilpotent-by-Abelian \(R^*\)-group, then every partial order on \(G\) can be extented to a linear order; (2) if
LONGOBARDI, Patrizia +2 more
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A group \(G\) is called \(R^*\)-group if for all \(n>0\) and elements \(g\) and \(x_1,\dots,x_n\) the equation \(g^{x_1 }\cdots g^{x_n }=1\) implies \(g=1\). The following results are proved: (1) if \(G\) is an Abelian-by-nilpotent as well as nilpotent-by-Abelian \(R^*\)-group, then every partial order on \(G\) can be extented to a linear order; (2) if
LONGOBARDI, Patrizia +2 more
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Journal of the London Mathematical Society, 1991
The authors say a group is homogeneous if any isomorphism between two of its finitely generated subgroups is induced by an automorphism. (In model theory there are also other versions of the concept of homogeneity; see the paper of \textit{B. I. Rose} and \textit{R. E. Woodrow} [Z. Math. Logik Grundlagen Math.
Cherlin, Gregory L., Felgner, Ulrich
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The authors say a group is homogeneous if any isomorphism between two of its finitely generated subgroups is induced by an automorphism. (In model theory there are also other versions of the concept of homogeneity; see the paper of \textit{B. I. Rose} and \textit{R. E. Woodrow} [Z. Math. Logik Grundlagen Math.
Cherlin, Gregory L., Felgner, Ulrich
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Algebra and Logic, 2015
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Information Sciences, 1993
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Under Solvable Groups as a Novel Generalization of Solvable Groups
Galoitica: Journal of Mathematical Structures and Applications, 2022The objective of this paper is to define a new generalization of solvable groups by using the concept of power maps which generalize the classical concept of powers (exponents). Also, it presents many elementary properties of this new generalization in terms of theorems.
Mohammad Abobala, Mehmet Celik
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Fuzzy Sets and Systems, 1999
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Mathematics of the USSR-Izvestiya, 1969
It is proved that in the class of radical groups containing solvable subgroups of some class s, the descending chain condition for subgroups is equivalent to the descending chain condition for solvable subgroups of class s.
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It is proved that in the class of radical groups containing solvable subgroups of some class s, the descending chain condition for subgroups is equivalent to the descending chain condition for solvable subgroups of class s.
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On the solvability of finite groups
Archiv der Mathematik, 1988In earlier papers the author has shown that normality of certain subgroups insures solvability or supersolvability. In this paper he shows that normality can be replaced by quasinormality. Let G be a finite group and define \(A_ 1=\{H\leq G:\) H has prime order or is cyclic of order \(4\}\), \(A_ 2=\{H\leq G:\) H has order 2p, p an odd prime\(\}\) and \
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The entropy of solvable groups
Ergodic Theory and Dynamical Systems, 2003The author proves that any finitely generated solvable group of zero entropy contains a nilpotent subgroup of finite index. In particular, any finitely generated solvable group of exponential growth is of uniformly exponential growth.
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Acta Mathematica Sinica, English Series, 2016
A finite group \(G\) is a \(D_{n}\)-group if and only if the number of non-linear irreducible characters of \(G\) is exactly \(n\) less than the number of their different degrees. \textit{Y. Berkovich} et al. [Proc. Am. Math. Soc. 115, No. 4, 955--959 (1992; Zbl 0822.20004)] classified \(D_{0}\)-groups and \textit{Y. Berkovich} and \textit{L. Kazarin} [
Liu, Yang, Lu, Zi Qun
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A finite group \(G\) is a \(D_{n}\)-group if and only if the number of non-linear irreducible characters of \(G\) is exactly \(n\) less than the number of their different degrees. \textit{Y. Berkovich} et al. [Proc. Am. Math. Soc. 115, No. 4, 955--959 (1992; Zbl 0822.20004)] classified \(D_{0}\)-groups and \textit{Y. Berkovich} and \textit{L. Kazarin} [
Liu, Yang, Lu, Zi Qun
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