The notion of almost centralizer and almost commutator are introduced and basic properties are established. They are used to study $\widetilde{\mathfrak M}\_c$-groups, i. e.groups for which every descending chain of centralizers each having infinite index in its predecessor stabilizes after finitely many steps. The Fitting subgroup of such groups is shown to be nilpotent and a theorem of Hall for nilpotent groups is generalized to ind-definable almost nilpotent subgroups of $\widetilde{\mathfrak M}\_c$-groups.

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几乎群论

引入了几乎集中器和几乎换向器的概念并建立了基本性质。它们用于研究 $\widetilde{\mathfrak M}\_c$-groups，即每个在其前身中具有无限索引的中心化器的每个下降链在有限多步后稳定的组。这些群的拟合子群被证明是幂零的，并且幂零群的霍尔定理被推广到 $\widetilde{\mathfrak M}\_c$-groups 的不可定义的几乎幂零子群。