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1.
A metacyclic group H can be presented as 〈α,β: αn = 1, βm = αt, βαβ?1 = αr〉 for some n, m, t, r. Each endomorphism σ of H is determined by \(\sigma(\alpha)=\alpha^{x_1}\beta^{y_1}, \sigma(\beta)=\alpha^{x_2}\beta^{y_2}\) for some integers x1, x2, y1, y2. We give sufficient and necessary conditions on x1, x2, y1, y2 for σ to be an automorphism. 相似文献
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GURMEET K BAKSHI SHALINI GUPTA INDER BIR S PASSI 《Proceedings Mathematical Sciences》2011,121(4):379-396
Given a group G of order p
1
p
2, where p
1, p
2 are primes, and
\mathbbFq\mathbb{F}_{q}, a finite field of order q coprime to p
1
p
2, the object of this paper is to compute a complete set of primitive central idempotents of the semisimple group algebra
\mathbbFq[G]\mathbb{F}_{q}[G]. As a consequence, we obtain the structure of
\mathbbFq[G]\mathbb{F}_{q}[G] and its group of automorphisms. 相似文献
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Christof Mackrodt 《manuscripta mathematica》1991,73(1):261-287
In the following paper homotopy representations (h.r.) for metacyclic groups of the form
相似文献
7.
Joseph Kirtland 《Expositiones Mathematicae》2004,22(4):395-398
A finite separable metacyclic 2-group G can be written as the semidirect product of a cyclic group with another cyclic group. Necessary and sufficient conditions are given for when all other split decompositions of G result in, up to isomorphism, this same semidirect product representation for G. 相似文献
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Johannes Huebschmann 《Archiv der Mathematik》1993,61(2):124-136
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On automorphisms of split metacyclic groups 总被引:1,自引:0,他引:1
Let D(m, n; k) be the semi-direct product of two finite cyclic groups and , where the action is given by yxy
−1 = x
k
. In particular, this includes the dihedral groups D
2m
. We calculate the automorphism group Aut (D(m, n; k)). 相似文献
11.
We study groups whose structure is similar to the structure of metacyclic groups. These groups play an important role in the investigation of groups with normal subgroups. 相似文献
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We describe non-orientable, octagonal embeddings for certain 4-valent, bipartite Cayley graphs of finite metacyclic groups, and give a class of examples for which this embedding realizes the non-orientable genus of the group. This yields a construction of Cayley graphs for which
is arbitrarily large, where and
are the orientable genus and the non-orientable genus of the Cayley graph.Work supported in part by the Research Council of Slovenia, Yugoslavia and NSF Contract DMS-8717441.Supported by NSF Contract DMS-8601760. 相似文献
14.
Hyo-Seob Sim 《代数通讯》2013,41(10):3773-3777
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《中国科学 数学(英文版)》2020,(7)
For an odd prime p, we give a criterion for finite p-groups whose nonnormal subgroups are metacyclic, and based on the criterion, the p-groups whose nonnormal subgroups are metacyclic are classified up to isomorphism. This solves a problem proposed by Berkovich. 相似文献
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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
19.
The automorphism group of a split metacyclic p-group 总被引:1,自引:0,他引:1
This paper finds the order, structure and presentation for the automorphism group of a split metacyclic p-group, where p is odd.
Received: 8 February 2006 相似文献
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