论文标题
最重要的力量指数，着色和楼梯的Metabelian群体不变
Invariants for metabelian groups of prime power exponent, colorings and stairs
论文作者
论文摘要
我们通过我们从整数网格$ \ mathbb {r} t immathbb {r Mathbb {r} {r} {r} {r imathbb {r mathbb {z r} \ times \ times \ times \ bb c \ bb c cub} Z {Z} {Z} {Z} {Z} { \ times \ mathbb {r} $。特别是我们改善了M.F.发现的界限Newman的订单为$ M（2,2^k）$。我们研究$ m（2，n）$的身份，这些身份提供了有关伯恩赛德组$ b（2，n）$和受限的伯恩赛德组$ r（2，n）$的信息。
We study the free metabelian group $M(2,n)$ of prime power exponent $n$ on two generators by means of invariants $M(2,n)'\to \mathbb{Z}_n$ that we construct from colorings of the squares in the integer grid $\mathbb{R} \times \mathbb{Z} \cup \mathbb{Z} \times \mathbb{R}$. In particular we improve bounds found by M.F. Newman for the order of $M(2,2^k)$. We study identities in $M(2,n)$, which give information about identities in the Burnside group $B(2,n)$ and the restricted Burnside group $R(2,n)$.
