Results 71 to 80 of about 5,201 (118)
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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
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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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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Mathematics of the USSR-Izvestiya, 1968
The immersion of normal subgroups in a solvable (or partially solvable) finite group is studied. In a series of cases the results obtained are presented in the form of a connection between a group and its group of operators.
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The immersion of normal subgroups in a solvable (or partially solvable) finite group is studied. In a series of cases the results obtained are presented in the form of a connection between a group and its group of operators.
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Characterization ofr-solvable groups
Siberian Mathematical Journal, 2000The following theorem is proven which generalizes a result by \textit{G.~Glauberman} [Ill. J. Math. 12, 76-98 (1968; Zbl 0182.35502)]: Let \(G\) be a finite \(K\)-group and let \(r\) be a prime divisor of the order of \(G\). Then \(G\) is \(r\)-soluble if and only if every pair of elements in \(G\) generates an \(r\)-soluble subgroup.
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