On a Problem of Minimal Non-fc-groups
نویسندگان
چکیده
In this paper Problem 17.13 by A.O. Asar in The Kourovka Notebook is studied which is ’Let G be a totally imprimitive p− group of finitary permutations on an infinite set. Suppose that the support of any cycle in the cyclic decomposition of every element of G is a block for G. Does G necessarily contain a minimal non− FC − subgroup?’ and an example of a group G satisfying these conditions but not having a minimal non − FC − subgroup is given. AMS Subject Classification: 20B35, 20F24, 20F05
منابع مشابه
Generalized Minimal Non-FC-Groups
Minimal non-FC-groups have been largely investigated and their structure is well-known. Minimal non-CC-groups, a first generalization of minimal non-FC-groups, have been investigated more recently and their complete description is still unknown. The present paper deals with generalizations of the notion of minimal non-FC-group in the context of locally nilpotent and locally solvable groups.
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