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We construct an $SU(3)_L \times U(1)_N$ gauge model based on an $S_{2L}$permutation symmetry for left-handed $\mu$ and $\tau$ families, which providesthe almost maximal atmospheric neutrino mixing and the large solar neutrinomixing of the LMA type. Neutrinos acquire one-loop radiative masses induced bythe radiative mechanism of the Zee type as well as tree level masses induced bythe type II seesaw mechanism utilizing interactions of lepton triplets with anSU(3)-sextet scalar. The atmospheric neutrino mixing controlled by thetree-level and radiative masses turns out to be almost maximal owing to thepresence of $S_{2L}$ supplemented by a $Z_4$ discrete symmetry. Thesesymmetries ensure the almost equality between the $\nu_e$-$\nu_\mu$ and$\nu_e$-$\nu_\tau$ radiative masses dominated by contributions from heavyleptons contained in the third members of lepton triplets, whose Yukawainteractions conserve $S_{2L}$, even after the spontaneous breaking. The solarneutrino mixing controlled by radiative masses including a $\nu_\mu$-$\nu_\tau$mass, which are taken to be the similar order, turns out to be described bylarge solar neutrino mixing angles.Comment: 29 pages, 13 figures, RevTex 4 Figures 5-13 in a PDF version are not  correcly reproduced. The tiny missing parts in Figures 2 and 3 were corrected  to be displayed. Added few refrences. To appear in Phys.Rev.

physical review. d. particles, fields, gravitation, and cosmology/physical review. d. particles and fields

<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi>S</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn><mml:mi>L</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math>permutation symmetry for left-handed<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>μ</mml:mi></mml:math>and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>τ</mml:mi></mml:math>families and neutrino …

S2Lpermutation symmetry for left-handedμandτfamilies and neutrino …