اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدEnumeration of groups whose order factorises in at most 4 primes
190
0
0.0
(
0
)
تأليف
Bettina Eick
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
Let $N(n)$ denote the number of isomorphism types of groups of order $n$. We consider the integers $n$ that are products of at most $4$ not necessarily distinct primes and exhibit formulas for $N(n)$ for such $n$.
قيم البحث
اقرأ أيضاً
The groups whose orders factorise into at most four primes have been described (up to isomorphism) in various papers. Given such an order n, this paper exhibits a new explicit and compact determination of the isomorphism types of the groups of order
n together with effective algorithms to enumerate, construct, and identify these groups. The algorithms are implemented for the computer algebra system GAP.
Let $v$ be a product of at most three not necessarily distinct primes. We prove that there exists no strong external difference family with more than two subsets in abelian group $G$ of order $v$, except possibly when $G=C_p^3$ and $p$ is a prime greater than $3 times 10^{12}$.
We prove that a group homomorphism $varphicolon Lto G$ from a locally compact Hausdorff group $L$ into a discrete group $G$ either is continuous, or there exists a normal open subgroup $Nsubseteq L$ such that $varphi(N)$ is a torsion group provided t
hat $G$ does not include $mathbb{Q}$ or the $p$-adic integers $mathbb{Z}_p$ or the Prufer $p$-group $mathbb{Z}(p^infty)$ for any prime $p$ as a subgroup, and if the torsion subgroups of $G$ are small in the sense that any torsion subgroup of $G$ is artinian. In particular, if $varphi$ is surjective and $G$ additionaly does not have non-trivial normal torsion subgroups, then $varphi$ is continuous. As an application we obtain results concerning the continuity of group homomorphisms from locally compact Hausdorff groups to many groups from geometric group theory, in particular to automorphism groups of right-angled Artin groups and to Helly groups.
Recent results of Qu and Tuarnauceanu describe explicitly the finite p-groups which are not elementary abelian and have the property that the number of their subgroups is maximal among p-groups of a given order. We complement these results from the b
ottom level up by determining completely the non-cyclic finite p-groups whose number of subgroups among p-groups of a given order is minimal.
Let $q$ be a prime, $n$ a positive integer and $A$ an elementary abelian group of order $q^r$ with $rgeq2$ acting on a finite $q$-group $G$. The following results are proved. We show that if all elements in $gamma_{r-1}(C_G(a))$ are $n$-Engel in $G
$ for any $ain A^#$, then $gamma_{r-1}(G)$ is $k$-Engel for some ${n,q,r}$-bounded number $k$, and if, for some integer $d$ such that $2^dleq r-1$, all elements in the $d$th derived group of $C_G(a)$ are $n$-Engel in $G$ for any $ain A^#$, then the $d$th derived group $G^{(d)}$ is $k$-Engel for some ${n,q,r}$-bounded number $k$. Assuming $rgeq 3$ we prove that if all elements in $gamma_{r-2}(C_G(a))$ are $n$-Engel in $C_G(a)$ for any $ain A^#$, then $gamma_{r-2}(G)$ is $k$-Engel for some ${n,q,r}$-bounded number $k$, and if, for some integer $d$ such that $2^dleq r-2$, all elements in the $d$th derived group of $C_G(a)$ are $n$-Engel in $C_G(a)$ for any $ain A^#,$ then the $d$th derived group $G^{(d)}$ is $k$-Engel for some ${n,q,r}$-bounded number $k$. Analogue (non-quantitative) results for profinite groups are also obtained.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
