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单词 Monster group
释义

Monster group

中文百科

魔群

Sporadic Finite Groups Showing (Sporadic) Subgroups

怪兽群英语:Monster group),或称友善巨人(the Friendly Giant)或费雪─格里斯怪兽(Fischer-Griess Monster),是一个有限单群,是26个散在群的其中之一,一般常将之记作MF1

怪兽群的阶是26个散在群中最大的,其阶为

有限单群的分类已完成(见有限单群分类一文)。有限单群的列表包含了十八类数量为可数无限的群,以及二十六个不包含在那十八类群中、尚未为其找到一个系统化模式的「散在群」。怪兽群是那26个散在群中,阶最大的群,同时除了六个群外,其余所有的散在群都是怪兽群的子集合。罗伯特‧格里斯(Robert Griess)将那六个不为怪兽群子集的群称为「贱民」(pariahs),并以「快乐大家族」(the happy family)一词称呼其他的散在群。

英语百科

Monster group 魔群

Diagram of the 26 sporadic simple groups, showing subquotient relationships.  The pariahs are the 4 groups on the right, and 2 groups (J4 and Ly) which are extensions of happy family groups. The diagram is correct, except that it incorrectly omits a line from O'N to M11.

In the area of modern algebra known as group theory, the Monster group M (also known as the Fischer–Griess Monster, or the Friendly Giant) is the largest sporadic simple group, having order

The finite simple groups have been completely classified. Every such group belongs to one of 18 countably infinite families, or is one of 26 sporadic groups that do not follow such a systematic pattern. The Monster group contains all but six of the other sporadic groups as subquotients. Robert Griess has called these 6 exceptions pariahs, and refers to the other 20 as the happy family.

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更新时间:2025/6/23 0:05:11