本文研究了满足K_S^2<=3χ-2 $且不含任何非正则根覆盖的一般S型极小曲面的代数基本群的结构.证明了：若K_S^2<=3χ-2，则S的代数基本群的阶至多为5，且等式仅在S是Godeaux曲面时才成立.我们还证明了如果K_S^2<= 3χ-3且S的代数基本群不是平凡的，则它是Z_2，或Z_2^2或Z_3。此外，在最后一种情况下，有：2<= x <=4，K^2=3 ×-3，这些可能性确实存在。
英文摘要：
We study the structure of the algebraic fundamental group for minimal surfaces of general type S satisfying K_S^2<=3χ-2$ and not having any irregular etale cover. We show that, if K_S^2<=3χ-2, then then the algebraic fundamental group of S has order at most 5, and equality only occurs if S is a Godeaux surface. We also show that if K_S^2<= 3χ-3 and the algebraic fundamental group of S is not trivial, then it is Z_2, or Z_2^2 or Z_3. Furthermore in this last case one has: 2<=χ<=4, K^2=3χ-3 and these possibilities do occur.
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