共查询到20条相似文献,搜索用时 15 毫秒
1.
We define a particular type of automorphisms called transvections on a finite finite abelian p-group Hp. It is proved that the subgroup E of the automorphism group Aut(Hp) of Hp generated by those transvections is normal in it, and that Aut(Hp) can be written as the product of E and some abelian subgroup K. The center of Aut(Hp) is also determined. 相似文献
2.
Jason Fulman 《Archiv der Mathematik》1999,73(1):1-10
Recent work on Hall polynomials is used to study the fixed space of a random automorphism of a finite abelian p-group. An expression is found for the chance that an automorphism of an abelian p-group of type l\lambda fixes only the identity. A formula is obtained for the chance that a given subgroup H of type n\nu is the fixed space of an automorphism of an abelian p-group of type (kl). There results generalize work of Rudvalis and Shinoda on the fixed space of an element of GL (n, q). 相似文献
3.
Let F
n
be the free group of rank n, let Aut(F
n
) be its automorphism group and let Out(F
n
) be its outer automorphism group. We show that every solvable subgroup of Out(F
n
) has a finite index subgroup that is finitely generated and free Abelian. We also show that every Abelian subgroup of Out(F
n
) has a finite index subgroup that lifts to Aut(F
n
). 相似文献
4.
M. J. Curran 《Archiv der Mathematik》2008,90(6):483-489
This note considers a finite group G = HK, which is a product of a subgroup H and a normal subgroup K, and determines subgroups of Aut G. The special case when G is a nonsplit metacyclic p-group, where p is odd, is then considered and the structure of its automorphism group Aut G is given.
Received: 13 September 2007, Revised: 22 November 2007 相似文献
5.
6.
Zvonimir Janko 《Mathematische Zeitschrift》2008,258(3):629-635
We determine here up to isomorphism the structure of any finite nonabelian 2-group G in which every two distinct maximal abelian subgroups have cyclic intersection. We obtain five infinite classes of such 2-groups
(Theorem 1.1). This solves for p = 2 the problem Nr. 521 stated by Berkovich (in preparation). The more general problem Nr. 258 stated by Berkovich (in preparation)
about the structure of finite nonabelian p-groups G such that A ∩ B = Z(G) for every two distinct maximal abelian subgroups A and B is treated in Theorems 3.1 and 3.2. In Corollary 3.3 we get a new result for an arbitrary finite 2-group. As an application
of Theorems 3.1 and 3.2, we solve for p = 2 a problem of Heineken-Mann (Problem Nr. 169 stated in Berkovich, in preparation), classifying finite 2-groups G such that A/Z(G) is cyclic for each maximal abelian subgroup A (Theorem 4.1).
相似文献
7.
In representation theory of finite groups, one of the most important and interesting problems is that, for a p-block A of a finite group G where p is a prime, the numbers k(A) and ℓ(A) of irreducible ordinary and Brauer characters, respectively, of G in A are p-locally determined. We calculate k(A) and ℓ(A) for the cases where A is a full defect p-block of G, namely, a defect group P of A is a Sylow p-subgroup of G and P is a nonabelian metacyclic p-group M
n+1(p) of order p
n+1 and exponent p
n
for
n \geqslant 2{n \geqslant 2}, and where A is not necessarily a full defect p-block but its defect group P = M
n+1(p) is normal in G. The proof is independent of the classification of finite simple groups. 相似文献
8.
A. Abdollahi 《代数通讯》2017,45(8):3636-3642
A longstanding conjecture asserts that every finite nonabelian p-group admits a noninner automorphism of order p. In this paper we give some necessary conditions for a possible counterexample G to this conjecture, in the case when G is a 2-generator finite p-group. Then we show that every 2-generator finite p-group with abelian Frattini subgroup has a noninner automorphism of order p. 相似文献
9.
Constantinos E. Kofinas 《代数通讯》2013,41(4):1575-1593
Let L be a relatively free nilpotent Lie algebra over ? of rank n and class c, with n ≥ 2; freely generated by a set 𝒵. Give L the structure of a group, denoted by R, by means of the Baker–Campbell–Hausdorff formula. Let G be the subgroup of R generated by the set 𝒵 and N Aut(L)(G) the normalizer in Aut(L) of the set G. We prove that the automorphism group of L is generated by GL n (?) and N Aut(L)(G). Let H be a subgroup of finite index in Aut(G) generated by the tame automorphisms and a finite subset X of IA-automorphisms with cardinal s. We construct a set Y consisting of s + 1 IA-automorphisms of L such that Aut(L) is generated by GL n (?) and Y. We apply this particular method to construct generating sets for the automorphism groups of certain relatively free nilpotent Lie algebras. 相似文献
10.
Let G be a finite group of order n, for some n\geqq 1 n\geqq 1 , and p be an odd prime number. In [5] Verardi has constructed a special p-group PG P_G of exponent p such that |PG|=p3n |P_G|=p^{3n} . In this paper, we calculate the order of Aut(PG) (P_G) and prove that Aut(PG) (P_G) is the semidirect product of two subgroups. 相似文献
11.
Yongge Tian 《Linear and Multilinear Algebra》2013,61(2):125-131
After recalling the definition and some basic properties of finite hypergroups—a notion introduced in a recent paper by one of the authors—several non-trivial examples of such hypergroups are constructed. The examples typically consist of n n×n matrices, each of which is an appropriate polynomial in a certain tri-diagonal matrix. The crucial result required in the construction is the following: ‘let A be the matrix with ones on the super-and sub-diagonals, and with main diagonal given by a 1…a n which are non-negative integers that form either a non-decreasing or a symmetric unimodal sequence; then Ak =Pk (A) is a non-negative matrix, where pk denotes the characteristic polynomial of the top k× k principal submatrix of A, for k=1,…,n. The matrices Ak as well as the eigenvalues of A, are explicitly described in some special cases, such as (i) ai =0 for all ior (ii) ai =0 for i<n and an =1. Characters ot finite abelian hypergroups are defined, and that naturally leads to harmonic analysis on such hypergroups. 相似文献
12.
A. A. Ryabchenko 《Siberian Mathematical Journal》2007,48(5):919-922
A group G is called a CI-group provided that the existence of some automorphism σ ∈ Aut(G) such that σ(A) = B follows from an isomorphism Cay(G, A) ? = Cay (G, B) between Cayley graphs, where A and B are two systems of generators for G. We prove that every finitely generated abelian group is a CI-group. 相似文献
13.
LetA={a
1, …,a
k} and {b
1, …,b
k} be two subsets of an abelian groupG, k≤|G|. Snevily conjectured that, when |G| is odd, there is a numbering of the elements ofB such thata
i+b
i,1≤i≤k are pairwise distinct. By using a polynomial method, Alon affirmed this conjecture for |G| prime, even whenA is a sequence ofk<|G| elements. With a new application of the polynomial method, Dasgupta, Károlyi, Serra and Szegedy extended Alon’s result to
the groupsZ
p
r
andZ
p
rin the casek<p and verified Snevily’s conjecture for every cyclic group. In this paper, by employing group rings as a tool, we prove that
Alon’s result is true for any finite abelianp-group withk<√2p, and verify Snevily’s conjecture for every abelian group of odd order in the casek<√p, wherep is the smallest prime divisor of |G|.
This work has been supported partly by NSFC grant number 19971058 and 10271080. 相似文献
14.
Martin R. Pettet 《Archiv der Mathematik》2008,91(4):289-299
Let G be an A-group (i.e. a group in which xx
α
= x
α
x for all and let denote the subgroup of Aut(G) consisting of all automorphisms that leave invariant the centralizer of each element of G. The quotient is an elementary abelian 2-group and natural analogies exist to suggest that it might always be trivial. It is shown that,
in fact, for any odd prime p and any positive integer r, there exist infinitely many finite pA-groups G for which has rank r.
Received: 23 March 2008, Revised: 20 May 2008 相似文献
15.
Thomas Ward 《Indagationes Mathematicae》1994,5(4)
Let (Σ, σ) be a
d-subshift of finite type. Under a strong irreducibility condition (strong specification), we show that Aut(Σ) contains any finite group. For
d-subshift of finite type without strong specification, examples show that topological mixing is not sufficient to give any finite group in the automorphism group in general: in particular, End(Σ) may be an abelian semigroup. For an example of a topologically mixing
2-subshift of finite type, the endomorphism semigroup and automorphism group are computed explicitly. This subshift has periodic-point permutations that do not extend to automorphisms. 相似文献
16.
P. Danchev 《Lithuanian Mathematical Journal》2007,47(2):129-134
We prove the following theorem: Any abelian p-group is an n-Σ-group which is a strong ω-elongation of a totally projective group by a p
ω+n
-projective group precisely when it is totally projective. In particular, each p-torsion p
ω+n
-projective n-Σ-group is a direct sum of countable p-groups of length not exceeding ω + n and vice versa. These two claims generalize our recent results in [6] and [7].
Published in Lietuvos Matematikos Rinkinys, Vol. 47, No. 2, pp. 155–162, April–June, 2007. 相似文献
17.
Let Out(F
n
) denote the outer automorphism group of the free group F
n
with n>3. We prove that for any finite index subgroup Γ<Out(F
n
), the group Aut(Γ) is isomorphic to the normalizer of Γ in Out(F
n
). We prove that Γ is co-Hopfian: every injective homomorphism Γ→Γ is surjective. Finally, we prove that the abstract commensurator Comm(Out(F
n
)) is isomorphic to Out(F
n
). 相似文献
18.
The simple group A
1(p
n
) is proved to be uniquely determined by the set of the orders of the maximal abelian subgroups of A
1(p
n
). 相似文献
19.
Let F n be the free group of rank n, and let Aut+(F n ) be its special automorphism group. For an epimorphism π : F n → G of the free group F n onto a finite group G we call the standard congruence subgroup of Aut+(F n ) associated to G and π. In the case n = 2 we fully describe the abelianization of Γ+(G, π) for finite abelian groups G. Moreover, we show that if G is a finite non-perfect group, then Γ+(G, π) ≤ Aut+(F 2) has infinite abelianization. 相似文献