论文标题
双重测序组
Doubly Sequenceable Groups
论文作者
论文摘要
给定一个序列$ {\ bf g}：g_0，\ ldots，g_ {m} $，在有限的组$ g $中，$ g_0 = 1_g $，让$ {\ bf \ bar g}：\ bar g_0，\ bar g_0，\ ldots，\ bar g_ par $ sequence $ sequence $ par $ par $ \ par $ \ ne $ \ ged， g_i = g_ {i-1}^{ - 1} g_i $，$ 1 \ leq i \ leq m $。我们说，如果存在$ g $中的序列$ {\ bf g} $，则$ g $是双重测序的，使得$ g $的每个元素在$ {\ bf g} $和$ {\ bf \ bar g} $中的每个元素中都完全显示出两次。如果一个$ g $是Abelian，奇数，可测序，可恢复或可跟动的，则$ g $是双重测序的。在本文中，我们表明，如果$ n $是一个奇数或可测序的组，而$ h $是一个阿贝里安组，那么$ n \ times h $是双重测序的。
Given a sequence ${\bf g}: g_0,\ldots, g_{m}$, in a finite group $G$ with $g_0=1_G$, let ${\bf \bar g}: \bar g_0,\ldots, \bar g_{m}$, be the sequence defined by $\bar g_0=1_G$ and $\bar g_i=g_{i-1}^{-1}g_i$ for $1\leq i \leq m$. We say that $G$ is doubly sequenceable if there exists a sequence ${\bf g}$ in $G$ such that every element of $G$ appears exactly twice in each of ${\bf g}$ and ${\bf \bar g}$. If a group $G$ is abelian, odd, sequenceable, R-sequenceable, or terraceable, then $G$ is doubly sequenceable. In this paper, we show that if $N$ is an odd or sequenceable group and $H$ is an abelian group, then $N \times H$ is doubly sequenceable.
