Sylow subgroupsFor a finite groupG, lets(G) denote the number of subgroups ofGandd(G) denote the number of divisors of |G|. In this paper, we prove that there does not exist a finite groupGsuch thatd(G) Jiakuan Luhttps://ror.org/02frt9q65grid.459584.10000 0001 2196 0260School of...
Let A be a finite group, and let p be a prime. Suppose that ps is the highest power of p dividing , where is the commutator subgroup of A , and that the type with of a Sylow p -subgroup of satisfies either or and . Let denote the number of subgroups of index d in A . If ...
I was wondering if there are any theorems that specify an exact number of subgroups that a group G has, maybe given certain conditions.The closest thing I...
The Number of Subgroups of a Finite Abelian p-group of Rank 4.doi:10.1063/1.4932475An explicit formula for the total number of subgroups of a finite abelian p-group up to rank three is known. In this paper, we investigate the total number of subgroups of a finite abelian p-group of ...
A Unimodality Result in the Enumeration of Subgroups of a Finite Abelian Group The number of subgroups of order pkin an abelian group G of order pnis a polynomial in p, αλ(k; p), determined by the type λ of G. It is well known that......
In other words, R has at most r log 2 r subgroups. This is the typical argument for bounding the number of subgroups of a finite group R . This bound is not too far off from the best possible. In fact, an elementary abelian 2-group of order r : = 2 a has [ a a 2 ] 2 :...
We deduce direct formulas for the total number of subgroups and the number of subgroups of a given order of the group $\Z_m imes \Z_n imes \Z_r imes \Z_s$, where $m,n,r,s\in \N$. The proofs are by some simple group theoretical and number theoretical arguments based on Goursat...
groupsubgroupdihedral groupfinite groupThe aim of? this paper is to compute the number of subgroups and? normal subgroups of the group $U_{2np}=\\langle a,b\\mid a^{2n}=b^{p}=e, aba^{-1}=b^{-1} angle$, where $p$ is an odd prime. Suppose $n=2^r\\prod_{1 \\leq i ...
Assume G is a group of order p^n,where p is an odd prime.Let sk(G)denote the number of subgroups of order p^k of G.We give a criterion for a p-group to be with sk(G)≤p^4 for each integer k satisfying 1≤k≤n.Moreover,such p-groups are classified. 关键词: finite p-gro...
Let ℤm be the group of residue classes modulo m. Let s(m, n) denote the total number of subgroups of the group ℤm × ℤn, where m and n are arbitrary positive integers. We derive asymptotic formulas for the sum ∑m,n≤x s(m, n) and for the corresponding sum restricted ...