ON A CONJECTURE OF MONTGOMERY
ON A CONJECTURE OF MONTGOMERY
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论蒙哥马利的猜想
DOI：
10.2307/1970061
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发表时间：
1957
影响因子：
4.9
通讯作者：
G. Mostow
中科院分区：
文献类型：
--
作者：
G. Mostow
在整篇论文中，G 表示紧李群，GC 表示 G 中单位元的连通分量。如果 G 是有限群，则 ord (G) 表示 G 中元素的数量。如果 g e G，则 ord (g) 表示 g 的通常阶。引理 1. 设 G 为紧李群，B 为整数。那么至多有有限数量的（互）非共轭子群 H 且 ord (H) < B. 证明。显然，只要证明最多存在有限个非共轭子群 H 且 ord (H) = B 就足够了。证明是通过反证法。假设 H1 , H2, ** 是互不共轭子群的无限序列
Throughout the paper, G denotes a compact Lie group and GC the connected component of the identity element in G. If G is a finite group, ord (G) denotes the number of elements in G. If g e G, ord (g) denotes the usual order of g. LEMMA 1. Let G be a compact Lie group and B an integer. Then there are at most a finite number of (mutually) non-conjugate subgroups H with ord (H) < B. PROOF. Obviously it suffices to prove that there exist at most a finite number of non-conjugate subgroups H with ord (H) = B. Proof is by contradiction. Suppose H1 , H2, * * is an infinite sequence of mutually non-conjugate subgroups