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A property of generalized McLain groups. (English) Zbl 1192.20036

Summary: In this short note we show that if \(S\) is a connected unbounded poset and \(R\) a ring with no zero divisors, then a generalized McLain group \(G(R,S)\) is a product of two proper normal subgroups.

MSC:

20H25 Other matrix groups over rings
20F19 Generalizations of solvable and nilpotent groups
20E07 Subgroup theorems; subgroup growth
20E22 Extensions, wreath products, and other compositions of groups
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References:

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