Growth series for the commutator subgroup
Growth series for the commutator subgroup
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换向子组的增长级数
DOI：
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发表时间：
1996
期刊：
影响因子：
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通讯作者：
Richard Sharp
中科院分区：
文献类型：
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作者：
M. Pollicott;Richard Sharp
本文研究了与曲面群的换位子群有关的增长级数。我们的结论是，这些增长序列是不合理的。0.引言在过去的几年中，有相当大的兴趣在增长系列的字长度的表面组G相对于一个有限的对称集的发电机去。如果对于h E G，我们让lhl表示h的字长（即，写h所需的来自Go的生成器的最小数量），并且写N（n）= #{h E GC：hl = n}，则增长级数由下式给出：
In this paper we study growth series associated to commutator subgroups of surface groups. We conclude that these growth series are not rational. 0. INTRODUCTION In the last few years there has been considerable interest in the growth series for the word length of surface groups G relative to a finite symmetric set of generators Go. If for h E G we let lhl denote the word length of h (i.e. the smallest number of generators from Go required in writing h) and write N(n) = #{h E GC: hl = n}, then the growth series is given by