一类广义幂零群

This paper considers such a group G which possesses nontrivial proper subgroups H 1 ,H 2 such that any proper subgroup of G not contained in H 1 ∪ H 2 is p-closed and obtains that if G is soluble,then the number of prime divisors contained in ｜G｜ is 2,3 or 4;if not,then it has a form x N where N/Φ（N） is a non-abelian simple group.Then the structure of such a group is determined for p = 2,H 1 = H 2 under some conditions.     

群定律与群簇

Letω1 and ω2 be two homogeneous words and suppose that they respectively define the varieties Vω1 and Vω2 of groups.Denote by θωi the standard exponent of ωi for i = 1,2,which was introduced in Ref.[1].We obtain that if Vω1 (∈) Vω2,then θω1|θω2.     

群定律与群簇

Let ω1 and ω 2 be two homogeneous words and suppose that they respectively define the varieties Vω 1 and Vω2 of groups. Denote by θωi the standard exponent of ωi for i =1, 2, which was introduced in Ref. [1]. We obtain that if Vω1 lohtian Vω2, then ω1θ｜θ ω2.