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This work is supported in part by NSERC Grant OGP0036631, Canada, and CNPq, Brasil 相似文献
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EPULIC Vladimir 《中国科学A辑(英文版)》2009,52(2):254-260
In this paper we investigate the title groups which we call isomaximal. We give the list of all isomaximal 2-groups with abelian
maximal subgroups. Further, we prove some properties of isomaximal 2-groups with nonabelian maximal subgroups. After that,
we investigate the structure of isomaximal groups of order less than 64. Finally, in Theorem 14. we show that the minimal
nonmetacyclic group of order 32 possesses a unique isomaximal extension of order 64.
This work was supported by Ministry of Science, Education and Sports of Republic of Croatia (Grant No. 036-0000000-3223) 相似文献
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M.M. Parmenter 《代数通讯》2013,41(10):3611-3617
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LetG be a group,ZG the integral group ring ofG andI(G) its augmentation ideal. Subgroups determined by certain ideals ofZG contained inI(G) are identified. For example, whenG=HK, whereH, K are normal subgroups ofG andH∩K⊆ζ(H), then the subgroups ofG determined byI(G)I(H)I(G), andI
3(G)I(H) are obtained. The subgroups of any groupG with normal subgroupH determined by (i)I
2(G)I(H)+I(G)I(H)I(G)+I(H)I2(G), whenH′⊆[H,G,G] and (ii)I(G)I(H)I(G) when degH
2(G/H′, T)≤1, are computed. the subgroup ofG determined byI
n(G)+I(G)I(H) whenH is a normal subgroup ofG withG/H free Abelian is also obtained 相似文献
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Let G be a finite group with cyclic Sylow subgroups. The integral group ring ZG is described as a multiple pullback ring, constructed from hereditary crossed product orders. 相似文献
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Partly supported by the Deutsche Forschungsgemeinschaft and the National Science Foundation. 相似文献
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V. P. Belkin 《Algebra and Logic》1978,17(3):171-179
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Peter V. Danchev 《Czechoslovak Mathematical Journal》2002,52(1):129-140
Suppose
is a commutative ring with identity of prime characteristic
and
is an arbitrary abelian
-group. In the present paper, a basic subgroup and a lower basic subgroup of the
-component
and of the factor-group
of the unit group
in the modular group algebra
are established, in the case when
is weakly perfect. Moreover, a lower basic subgroup and a basic subgroup of the normed
-component
and of the quotient group
are given when
is perfect and
is arbitrary whose
is
-divisible. These results extend and generalize a result due to Nachev (1996) published in Houston J. Math., when the ring
is perfect and
is
-primary. Some other applications in this direction are also obtained for the direct factor problem and for a kind of an arbitrary basic subgroup. 相似文献
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Martin Hertweck 《Proceedings of the American Mathematical Society》2008,136(5):1539-1547
For finite nilpotent groups and , and a -adapted ring (the rational integers, for example), it is shown that any isomorphism between the centers of the group rings and is monomial, i.e., maps class sums in to class sums in up to multiplication with roots of unity. As a consequence, and have identical character tables if and only if the centers of their integral group rings and are isomorphic. In the course of the proof, a new proof of the class sum correspondence is given.
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For a large class of groups G a precise congruence subgroup of the group generated by the bicyclic units of the integral group ring ZG is determined. As an application an upper bound is calculated for the index in the unit group of ZG for the group generated by the Bass cyclic units and the bicyclic units. 相似文献
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Carmela Musella 《Rendiconti del Circolo Matematico di Palermo》2001,50(1):129-136
A subgroupH of a groupG is said to bealmost normal inG if it has only finitely many conjugates inG. The setan(G) of almost normal subgroups ofG is a sublattice of the lattice of all subgroups ofG. Isomorphisms between lattices of almost normal subgroups ofFC-soluble groups are considered in this paper. In particular, properties of images of normal subgroups under such an isomorphism
are investigated. 相似文献
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In this note, we show that when is a torsion group the second center of the group of units of the integral group ring is generated by its torsion subgroup and by the center of . This extends a result of Arora and Passi (1993) from finite groups to torsion groups, and completes the characterization of hypercentral units in when is a torsion group.
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Stanley Orlando Juriaans 《代数通讯》2013,41(12):4905-4913
Several special cases of the conjectures of Bovdi and Zassenhaus are proved. We also deal with special cases of the following conjecture: let α be a torsion unit of the integral group ring ZZG and m the smallest positive integer such that αm ∈G then, m is a divisor of the exponent of the quotient group G/Z(G) provided this exponent is finite 相似文献