Results 271 to 280 of about 8,796 (305)
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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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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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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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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
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
Alexandre Borovik, Ali Nesin
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