Geodesic
Product varieties of $m$-groups
Algebra i logika, Tome 51 (2012) no. 6, pp. 722-733

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A new concept of mimicking is introduced. We point out representations that mimic a variety $\mathcal A$ of Abelian $m$-groups and a variety $\mathcal I$ of $m$-groups defined by an identity $x_*=x^{-1}$. It is proved that if a variety $\mathcal U$ of $m$-groups is generated by some class of $m$-groups, and a variety $\mathcal V$ of $m$-groups is mimicked by some class of $m$-groups, then their product $\mathcal{U\cdot V}$ is generated by wreath products of groups in the respective classes. For every natural $n$, we construct $m$-groups generating varieties $\mathcal I_n=(\mathcal I^{n-1})\cdot\mathcal I$ and $\mathcal A_n=(\mathcal A^{n-1})\cdot\mathcal A$.
Mots-clés : $m$-group
Keywords: representation, mimicking, wreath product, product of varieties. 
@article{AL_2012_51_6_a1,
     author = {A. V. Zenkov},
     title = {Product varieties of $m$-groups},
     journal = {Algebra i logika},
     pages = {722--733},
     publisher = {mathdoc},
     volume = {51},
     number = {6},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2012_51_6_a1/}
}
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A. V. Zenkov. Product varieties of $m$-groups. Algebra i logika, Tome 51 (2012) no. 6, pp. 722-733. http://geodesic.mathdoc.fr/item/AL_2012_51_6_a1/