  Many-body variational ground-state wave function of two-dimensional electron
system (2DES), localized in the main strip (MS)$L_{x}^{\square} \times L_{y}$
of the finite width $L_{x}^{\square}=\sqrt{2 \pi m} \ell_{0}$ (and the periodic
boundary condition (PBC) imposed along $x-$direction), is presented at the
fractional and the integral filling factors $\nu=1/m$ for two different ion
backgrounds: microscopical uniform ion background (UIB) and classical ion
jellium background (IJB); $\ell_{0}$ is the magnetic length, $m=2\ell+1$ and
$\ell=0, 1, 2,...$. It is shown that the ground-state and the lowest
excited-state can correspond to partial crystal-like correlation order among
$N$ electrons of the main region (MR) $L_{x} \times L_{y}$; then the study of
2DES of $N$ electrons within MR is exactly reduced to the treatment of 2DES of
$\tilde{N}=N L_{x}^{\square}/L_{x}$ electrons localized within MS, with PBC
along $x$. The ground-state manifests the broken symmetry liquid-crystal state
with 2DES density that is periodic along the $y-$ direction, with the period
$L_{x}^{\square}/m$, and independent of $x$. For IJB, at $m=3, 5$, the
ground-state has essentially lower energy per electron than the Laughlin,
uniform liquid, ground-state (the Laughlin model uses IJB); the same holds at
$m=1$. Obtained compound exciton and compound spin-exciton states show finite
excitation gaps. The excited compound electron (hole) is composed, within MS,
from $m$ strongly correlated quasielectrons (quasiholes) of the charge $e/m$
($-e/m$. Quantized Hall conductance $\sigma_{H}=e^{2}/(2 m \pi \hbar)$ is
obtained. The theory is in good agreement with experiments.
