By using cyclic subgroups of order 4 with semi cover - avoiding property in the group, some known results are generalized ( 1 ) suppose that x is a weak left Engle element for every element x of G with prime order, 2 ∈(G) ,if 〈 x 〉 is semi cover - avoiding in G for every element x of G with order 4, Then G is nilpotent. (2) suppose that N〈3 G, G/N , G is nilpotent, 2∈ π(G). If x is a weak left Engle element for every element x of N with prime order , and 〈 x 〉 is semi cover - avoiding in G for every element x of N with order 4, Then G is nilpotent.%利用4阶循环子群具有半覆盖远离性的性质得到了：（1）如果群G的每个素数阶元都是群G的弱左Engle元，2∈1T（G），群G的每个4阶循环子群在群G中具有半覆盖远离性，则G幂零．（2）设N〈3G，GIN幂零，2∈π（G），若N的素数阶元均为群G的弱左Engle元，且N的每个4阶循环子群也在群G中具有半覆盖远离性，则G幂零．
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