论文标题
有限的阿贝尔组实现的变性和图的顺序
Degenerations and order of graphs realized by finite abelian groups
论文作者
论文摘要
令G_1和G_2为两组。如果一个组同构φ：g_1 \ longrightArrow g_2将g_1中的a \映射到g_2中的b \中，以使φ（a）= b映射为φ（a）= b，那么我们说对b的退化，如果g_1的每个元素都会降低到g_2中的元素，那么我们说g_1 demenerates to g_1 demenerates to g_1 demenerates to g__2。在本文中，我们研究了图中的变性，并表明组中的变性是图中变性的一种特殊情况。我们在图中表现出一些有趣的变性属性。我们使用这个概念呈现有限阿贝尔群体实现的图表的图形表示。我们将所有图表的t_p_1 \ dots t_p_n上的某些部分订单讨论了有限的Abelian P_R组所实现的所有图，其中每个p_r，1 \ leq r \ leq n是一个质量数字。我们表明，可以用POSET T_P_1 \ DOTS T_P_N中的年轻图的饱和链来识别等级n的每个有限的Abelian P_R组。我们提出了一个组合公式，该公式代表了对称群体的投影表示程度。该公式确定T_P_1 \ CDOTS T_P_N中不同饱和链的数量以及不同订单的有限ABELIAN组的数量。
Let G_1 and G_2 be two groups. If a group homomorphism φ: G_1 \longrightarrow G_2 maps a \in G_1 into b \in G_2 such that φ(a) = b, then we say a degenerates to b and if every element of G_1 degenerates to elements in G_2, then we say G_1 degenerates to G_2. In this paper, we study degeneration in graphs and show that degeneration in groups is a particular case of degeneration in graphs. We exhibit some interesting properties of degeneration in graphs. We use this concept to present a pictorial representation of graphs realized by finite abelian groups. We discus some partial orders on the set T_p_1 \dots T_p_n of all graphs realized by finite abelian p_r-groups, where each p_r, 1 \leq r \leq n, is a prime number. We show that each finite abelian p_r-group of rank n can be identified with saturated chains of Young diagrams in the poset T_p_1 \dots T_p_n. We present a combinatorial formula which represents the degree of a projective representation of a symmetric group. This formula determines the number of different saturated chains in T_p_1 \cdots T_p_n and the number of finite abelian groups of different orders.
