Results 281 to 290 of about 116,152 (330)
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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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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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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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CHARACTERIZATION OF SOLVABLE GROUPS AND SOLVABLE RADICAL
International Journal of Algebra and Computation, 2013We give a survey of new characterizations of finite solvable groups and the solvable radical of an arbitrary finite group which were obtained over the past decade. We also discuss generalizations of these results to some classes of infinite groups and their analogues for Lie algebras. Some open problems are discussed as well.
Grunewald, F. +2 more
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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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Mathematische Nachrichten, 1984
Let G be a finite solvable group. G is known to be nilpotent iff \(C_ G(M/N)=G\) holds for each chief factor M/N of G. A contrary situation takes place if \(C_ G(M/N)=M\) for each chief factor M/N of G. Groups G satisfying this condition are said to be abnilpotent. Those groups were already considered by \textit{T. O. Hawkes} [Trans. Am. Math. Soc. 214,
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Let G be a finite solvable group. G is known to be nilpotent iff \(C_ G(M/N)=G\) holds for each chief factor M/N of G. A contrary situation takes place if \(C_ G(M/N)=M\) for each chief factor M/N of G. Groups G satisfying this condition are said to be abnilpotent. Those groups were already considered by \textit{T. O. Hawkes} [Trans. Am. Math. Soc. 214,
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Algebra and Logic, 2015
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zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Canadian Journal of Mathematics, 1973
Let K[G] denote the group ring of G over the field K. One of the interesting problems which arises in the study of such rings is to find precisely when they satisfy polynomial identities. This has been solved for char K = 0 in [1] and for char K = p > 0 in [3]. The answer is as follows.
Passi, I. B. S. +2 more
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Let K[G] denote the group ring of G over the field K. One of the interesting problems which arises in the study of such rings is to find precisely when they satisfy polynomial identities. This has been solved for char K = 0 in [1] and for char K = p > 0 in [3]. The answer is as follows.
Passi, I. B. S. +2 more
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1994
Abstract The structure theory of solvable groups of finite Morley rank is in a quite satisfactory state, though by no means as detailed as the theory available in the algebraic case [189). We obtain the conjugacy of Sylow subgroups for arbitrary primes (whereas the general theory of the next chapter works only for the prime 2) as well as
Alexandre Borovik, Ali Nesin
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Abstract The structure theory of solvable groups of finite Morley rank is in a quite satisfactory state, though by no means as detailed as the theory available in the algebraic case [189). We obtain the conjugacy of Sylow subgroups for arbitrary primes (whereas the general theory of the next chapter works only for the prime 2) as well as
Alexandre Borovik, Ali Nesin
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Journal of Group Theory, 2010
Let \(G\) be a finite group. An element \(x\in G\) is called rational (resp. semi-rational, inverse semi-rational), if all generators of the group \(\langle x\rangle\) are contained in a single conjugacy class of \(G\) (resp. in a union of two conjugacy classes of \(G\), in \(x^G\cup(x^{-1})^G\)). If all elements of \(G\) are rational (resp.
D. Chillag, DOLFI, SILVIO
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Let \(G\) be a finite group. An element \(x\in G\) is called rational (resp. semi-rational, inverse semi-rational), if all generators of the group \(\langle x\rangle\) are contained in a single conjugacy class of \(G\) (resp. in a union of two conjugacy classes of \(G\), in \(x^G\cup(x^{-1})^G\)). If all elements of \(G\) are rational (resp.
D. Chillag, DOLFI, SILVIO
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