On F-inverse covers of inverse monoids

详细信息    查看全文

• 作者：K. Auinger and M.B. Szendrei
• 刊名：Journal of Pure and Applied Algebra
• 出版年：2006
• 出版时间：March 2006
• 年：2006
• 卷：204
• 期：3
• 页码：493-506
• 全文大小：183 K

文摘

It is shown that each finite inverse monoid admits a finite F-inverse cover if and only if the same is true for each finite combinatorial strict inverse semigroup with an identity adjoined if and only if the same is true for the Margolis–Meakin expansion M(H) of each finite elementary abelian p-group H for some prime p. Additional equivalent conditions are given in terms of the existence of locally finite varieties of groups having certain properties. Ultimately, the problem of whether each finite inverse monoid admits a finite F-inverse cover, is reduced to a question concerning the Kostrikin–Zelmanov varieties of all locally finite groups of exponent dividing n.