It is proved that if G is an \(\mathfrak {X}\)-group of infinite rank whose proper subgroups of infinite rank are Baer groups, then so are all proper subgroups of G, where \(\mathfrak {X}\) is the class defined by N.S. Černikov as the closure of the class of periodic locally graded groups by the closure operations \(\varvec{\acute{P}}\), \(\varvec{\grave{P}}\) and \( \varvec{L}\). We prove also that if a locally graded group, which is neither Baer nor Černikov, satisfies the minimal condition on non-Baer subgroups, then it is a Baer-by-Černikov group which is a direct product of a p-subgroup containing a minimal non-Baer subgroup of infinite rank, by a Černikov nilpotent \(p^{\prime }\)-subgroup, for some prime p. Our last result states that a group is locally graded and has only finitely many conjugacy classes of non-Baer subgroups if, and only if, it is Baer-by-finite and has only finitely many non-Baer subgroups.

证明如果G是一个无限级\（\ mathfrak {X} \）-群，其无穷等级的适当子群是Baer群，那么G的所有适当子群也都是，其中\（\ mathfrak {X} \ ）是NSČernikov定义的类，它是通过闭包运算\（\ varvec {\ acute {P}} \），\（\ varvec {\ grave {P}} \\和\（\ varvec {L} \）。我们还证明，如果既不是Baer也不是Černikov的本地分级组满足非Baer子组的最小条件，则它是Baer byČernikov组，它是p的直接乘积-subgroup包含一个无限阶的最小非Baer子组，由Černikov幂\（p ^ {\ prime} \）- subgroup组成，它包含一些素数p。我们的最后结果表明，一个组是局部分级的，并且仅当它是有限个Baer且仅有限个非Baer子组时，才有非Baer子组的共轭类。