Letwbe a group-word. Given a groupG, we denote byw(G) the verbal subgroup corresponding to the wordw, that is, the subgroup generated by the setGwof allw-values inG. The wordwis called concise in a class of groupsXifw(G) is finite wheneverGwis finite for a groupG∈χ. It is a...
subgroup lattice of G. Different properties and problems related to this ratio are studied throughout the paper. We determine the second minimum value of β on the class of p-groups of order pn, where n ≥ 3 is an integer. We show that the set containing the quantities β(G), where ...
1) order of an element to a subgroup 元素对于子群的阶 1. In this paper,the author discusses the order of an element of periodic groups and free groups,studies the order of an element of the additive group of a ring and establishes the concept of the characteristic number of a ring,and...
2) Step normal fuzzy subgroup 阶梯模糊子群3) fuzzy subgroups 模糊子群 1. A note on fuzzy relations and fuzzy subgroups; 关于模糊关系与模糊子群的注记 2. we give definition of normal α+β-fuzzy subgroups and discuss some properties of α+β-fuzzy subgroups. 引入了一种称之为α+β—...
These results suggest that the fraternal birth order effect may apply to a subset of gay men who have a bottom anal sex role preference and that this subgroup is more gender-nonconforming. However, there were no significant associations between fraternal birth order and gender nonconformity at ...
section class species bracket variety genus generation rank(s) league rubric grade division breed description manner subgroup kidney specialty nature race subdivision branch subclass like subspecies speciality heading label title feather ilk order2 of 2 verb...
Four theorems are proved stating, under various additional hypotheses, that if G is a group containing a finite subgroup H with finite centralizer C G (H), then G is finite, and its order is bounded in terms of the orders of H and C G (H). The proofs use elementary methods. In fac...
No group of order36 is simple.Such a group G has either one or four subgroups of order 9.If there is only one such subgroup,it is normal in G.If there are four such subgroups,let H and K be two of them.H∩K must have at least 3elements,or Hk would have to have 81elements,...
6.28.LetGbe a group of order #G=75. (a)Prove thatGhas a subgroupHwith all three of the following properties: (1)Hhas order #H=25. (2)His a normal subgroup ofG. (3)His abelian. (b)Suppos...
structure of2.G/we get infinitelymany groups.In subsection 4owe consider a similar problem. In [Ber25,ń48] the2-groupsGhave been considered which have exactly one abelian subgroup of type.4;2/.Itwasshown that eitherj2.G/jD8(and thenGis isomorphic to one of the groups inLemma 42.1) ...