1.A distinct group within a group; a subdivision of a group. 2.A subordinate group. 3.MathematicsA group that is a subset of a group. tr.v.sub·grouped,sub·group·ing,sub·groups To divide into subgroups. American Heritage® Dictionary of the English Language, Fifth Edition. Copyright...
finite abelian p-groupgenerating functionIn this paper, we provide an explicit formula for the number of subgroups series of group Z_pm 脳 Z_pn which contains a subgroup of order p where pisa prime number and , n E Z~+ . This is achieved by using the maximal chains of subgroups which...
Let G be a finite group with identity e. The subgroup intersection graph Gamma_SI (G) of G isa graph with vertex set G e and two distinct vertices x and y are adjacent if and only if | i ∩ | | > 1. In this paper, we obtain a lower bound for the indepe
Let GG be a noncyclic abelian group, then it must include a subgroup which is isomorphic to Zp×ZpZp×Zp. Clearly in taht case the subgroup of order pp is not uniqe which is a contradiction. Share Cite Follow answered Jul 10, 2014 at 20:07 mesel 15k22 gold badges2727 silver badge...
Let G be a finiteAbelian group,an ideal in the grouping Zpr is called an Abelian code over Zpr. 设G为有限阿贝尔群,群环Zpr[G]中的理想称为Zpr上的阿贝尔码。 2. The security~ of these cryptosystems is based on the dificulty in solving descrete logarithms withAbelian group. ...
3) maximal Abelian subgroup 极大交换子群 1. Let G be a finite group, M(G) the set of maximal Abelian subgroup of G, i. 设G为有限群,G的极大交换子群的阶的集合记为M(G),即M(G)={|N||N交换,N<G,且对M≤G,M交换,若N≤M,则G=M或N=M}。 更多例句>> ...
abelian groupThe intersection graph of subgroups of a finite groupGis a graph whose vertices are all nontrivial subgroups ofGand in which two distinct verticesHandKare adjacent if and only ifH∩K≠1. The non-orientable genus of a graphΓis the smallest positive integernsuch thatΓcan be ...
Abelian groups whose subgroup lattice is the union of two intervals In this note we characterize the abelian groupsGwhich have two different proper subgroupsNandMsuch that the subgroup latticeL(G)=[0, M][N, G] is the union ... S Breaz,G C?Lug?Reanu - 《Journal of the Australian Mat...
A non-empty subset B of an arbitrary Abelian group G is said to be periodic, if there exists a non-trivial (≠{0}) subgroup P of G such that B+P=B. It means that B is the union of one or more P-cosets. If so P is called a period of B. Clearly the definition does not ...
Prove that every quotient group of an abelian group is abelian and that every quotient group of a cyclic group is cyclic. If G is an abelian group, prove that pG = {px| x element of G} is a subgroup of G? If G is an abelian group, prove that G(p) is ...