scholarly journals Almost Hamiltonian Groups

2005 ◽  
Vol 48 (1-2) ◽  
pp. 44-49
Author(s):  
Tuval Foguel ◽  
Pantelimon Stănică
Keyword(s):  
Hamiltonian Groups

Quantum solution to the hidden subgroup problem for Poly-Near-Hamiltonian groups

2004 ◽  
Vol 4 (3) ◽  
pp. 229-235
Author(s):  
D. Gavinsky
Keyword(s):  
Quantum Computing ◽  
Efficient Algorithm ◽  
Abelian Groups ◽  
Hidden Subgroup Problem ◽  
Subgroup Problem ◽  
Hamiltonian Groups ◽  
Quantum Solution

The Hidden Subgroup Problem (HSP) has been widely studied in the context of quantum computing and is known to be efficiently solvable for Abelian groups, yet appears to be difficult for many non-Abelian ones. An efficient algorithm for the HSP over a group \f G\ runs in time polynomial in \f{n\deq\log|G|.} For any subgroup \f H\ of \f G, let \f{N(H)} denote the normalizer of \f H. Let \MG\ denote the intersection of all normalizers in \f G (i.e., \f{\MG=\cap_{H\leq G}N(H)}). \MG\ is always a subgroup of \f G and the index \f{[G:\MG]} can be taken as a measure of ``how non-Abelian'' \f G is (\f{[G:\MG] = 1} for Abelian groups). This measure was considered by Grigni, Schulman, Vazirani and Vazirani, who showed that whenever \f{[G:\MG]\in\exp(O(\log^{1/2}n))} the corresponding HSP can be solved efficiently (under certain assumptions). We show that whenever \f{[G:\MG]\in\poly(n)} the corresponding HSP can be solved efficiently, under the same assumptions (actually, we solve a slightly more general case of the HSP and also show that some assumptions may be relaxed).

On a Generalization of Hamiltonian Groups and a Dualization of PN-Groups

2013 ◽  
Vol 41 (5) ◽  
pp. 1608-1618 ◽  
Author(s):  
Zhencai Shen ◽  
Jinshan Zhang ◽  
Wujie Shi
Keyword(s):  
Hamiltonian Groups

ZETA FUNCTION OF THE BURNSIDE RING FOR HAMILTONIAN GROUPS

2015 ◽  
Vol 37 (2) ◽  
pp. 125-132
Author(s):  
David Villa-Hernández ◽  
César Cejudo Castilla
Keyword(s):  
Zeta Function ◽  
Burnside Ring ◽  
Hamiltonian Groups

Subgroups like Wielandt's in finite soluble groups

1990 ◽  
Vol 107 (2) ◽  
pp. 239-259 ◽  
Author(s):  
R. A. Bryce
Keyword(s):  
Internal Structure ◽  
Direct Product ◽  
Periodic Group ◽  
Quaternion Group ◽  
Soluble Groups ◽  
Parent Group ◽  
Dedekind Group ◽  
Points Of View ◽  
Hamiltonian Groups

In 1935 Baer[1] introduced the concept of kern of a group as the subgroup of elements normalizing every subgroup of the group. It is of interest from three points of view: that of its structure, the nature of its embedding in the group, and the influence of its internal structure on that of the whole group. The kern is a Dedekind group because all its subgroups are normal. Its structure is therefore known exactly (Dedekind [7]): if not abelian it is a direct product of a copy of the quaternion group of order 8 and an abelian periodic group with no elements of order 4. As for the embedding of the kern, Schenkman[13] shows that it is always in the second centre of the group: see also Cooper [5], theorem 6·5·1. As an example of the influence of the structure of the kern on its parent group we cite Baer's result from [2], p. 246: among 2-groups, only Hamiltonian groups (i.e. non-abelian Dedekind groups) have nonabelian kern.

On the structure of generalized Hamiltonian groups

2000 ◽  
Vol 75 (5) ◽  
pp. 328-337 ◽  
Author(s):  
L.-C. Kappe ◽  
D.M. Reboli
Keyword(s):  
Hamiltonian Groups
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