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On quasivarieties of nilpotent Moufang loops. II

Vasile I. Ursu (2012)

Commentationes Mathematicae Universitatis Carolinae

In this part of the paper we study the quasiidentities of the nilpotent Moufang loops. In particular, we solve the problem of finite basis for quasiidentities in the finitely generated nilpotent Moufang loop.

On R -conjugate-permutability of Sylow subgroups

Xianhe Zhao, Ruifang Chen (2016)

Czechoslovak Mathematical Journal

A subgroup H of a finite group G is said to be conjugate-permutable if H H g = H g H for all g G . More generaly, if we limit the element g to a subgroup R of G , then we say that the subgroup H is R -conjugate-permutable. By means of the R -conjugate-permutable subgroups, we investigate the relationship between the nilpotence of G and the R -conjugate-permutability of the Sylow subgroups of A and B under the condition that G = A B , where A and B are subgroups of G . Some results known in the literature are improved and...

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