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On the theory of groups of $W\sb q$-symmetry. (Russian)
Authors: Lungu A. P.
Abstract
The crosed-quasihomomorphism $\alpha$ of a group $G$ onto a subset $W^\prime$ of a group $W=\overline{\prod}_{g_i\in G} P^{g_i}$ (where $P^{g_i}\simeq P$) is defined by $\alpha(g_ig_j)=\left[\alpha(g_i)\right]^{g_j}*\overset\leftharpoonup\to{\tau_{g_i}}\left [\alpha (g_j)\right ]=w_i^{g_j} *\overset\leftharpoonup\to{\tau_{g_i}}(w_j)=w_k$, where $ g_i,g_j\in G; w_i,w_j,w_k\in W^\prime; w_i^{g_j}(g_s)=w_i(g_jg_s)$ a $g_j$-left-translation of componnents; $\overset\leftharpoonup\to{\tau_{g_i}}=\tau (g_i)$, $\tau : G\rightarrow \text{Aut }W$ a homomorphism. The general properties of the map $\alpha $ as well as the general structure of the $W^\prime $-semi-minor and $W^\prime$-pseudo-minor groups of $W_q$-symmetry $G^{(W_q)}$ are examined. One method of derivation of semi-minor and pseudo-minor groups of $W_q$-symmetry from permutation group $P$ and classical symmetry group $G$ is developed. This method is based on crosed-quasihomomorphisms.Universitatea de Stat din Moldova
str. Mateevici 60, Chişinău, MD-2009 Moldova
str. Mateevici 60, Chişinău, MD-2009 Moldova
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