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- W2950620478 abstract "A class of groups C is root in a sense of K. W. Gruenberg if it is closed under taking subgroups and satisfies the Gruenberg condition: for any group X and for any subnormal sequence Z leqslant Y leqslant X with factors in C, there exists a normal subgroup T of X such that T leqslant Z and X/T in C. We prove that a class of groups is root if, and only if, it is closed under subgroups and Cartesian wreath products. Using this result we prove also that, if C is a nontrivial root class of groups closed under taking quotient groups and G = <A*B; H=K, varphi> is the generalized free product of two nilpotent C-groups A and B possessing varphi-compartible central series, then G is residually a solvable C-group." @default.
- W2950620478 created "2019-06-27" @default.
- W2950620478 creator A5017775764 @default.
- W2950620478 date "2013-08-05" @default.
- W2950620478 modified "2023-10-16" @default.
- W2950620478 title "A characterization of root classes of groups" @default.
- W2950620478 cites W2036423535 @default.
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- W2950620478 doi "https://doi.org/10.48550/arxiv.1308.1039" @default.
- W2950620478 hasPublicationYear "2013" @default.
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