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61.
《代数通讯》2013,41(5):2357-2379
Abstract Restrictions of irreducible representations of classical algebraic groups to root A 1-subgroups, i.e., subgroups of type A 1 generated by root subgroups associated with two opposite roots, are studied. Composition factors of such restrictions are found in the following cases: for groups of types A n with n > 2 and D n , for groups of type B n , n > 2, and long root subgroups, for groups of type C n , n > 2, and short root subgroups, and for p-restricted representations of A 2(K), C 2(K) (recall that B 2(K) ? C 2(K)), and of B n (K), n > 2, and short root subgroups. Here we assume that p > 2 for G = B n (K) or C n (K). 相似文献
62.
《代数通讯》2013,41(7):3471-3486
Abstract Taking G to be a Chevalley group of rank at least 3 and U to be the unipotent radical of a Borel subgroup B,an extremal subgroup A is an abelian normal subgroup of U which is not contained in the intersection of all the unipotent radicals of the rank 1 parabolic subgroups of G containing B. If there is an unique rank 1 parabolic subgroup P of G containing B with the property that A is not contained in the unipotent radical of P,then A is called a unique node extremal subgroup. In this paper we investigate the embedding of unique node extremal subgroups in U and prove that,apart from some specified cases,such a subgroup is contained in the unipotent radical of a certain maximal parabolic subgroup. 相似文献
63.
J. Cimprič 《代数通讯》2013,41(1):103-119
A subgroup H is called Q-supplemented in a finite group G, if there exists a subgroup K of G such that G = HK and H ∩ K is contained in H QG , where H QG is the maximal quasinormal subgroup of G contained in H. In this article, we investigate the influence of Q-supplementation of some primary subgroups in finite groups. Some recent results are generalized. 相似文献
64.
Let K be a field of characteristic p > 0, let L be a restricted Lie algebra and let R be an associative K-algebra. It is shown that the various constructions in the literature of crossed product of R with u(L) are equivalent. We calculate explicit formulae relating the parameters involved and obtain a formula which hints at a noncommutative version of the Bell polynomials. 相似文献
65.
In this article we construct free groups and subgroups of finite index in the unit group of the integral group ring of a finite non-Abelian group G for which every nonlinear irreducible complex representation is of degree 2 and with commutator subgroup G′ a central elementary Abelian 2-group. 相似文献
66.
Tararin has shown that a non-Abelian group G admits a nonzero finite number of distinct right-orders if and only if G is equipped with a Tararin-type series of some length n. Further, a group which has a Tararin-type series of length n admits 2 n right-orders. It is known that a group has two right-orders if and only if it is torsionfree Abelian of rank 1. Here we completely classify the groups which admit either four or eight right-orders. 相似文献
67.
We classify two types of finite groups with certain normality conditions, namely SSN groups and groups with all noncyclic subgroups normal. These conditions are key ingredients in the study of the multiplicative Jordan decomposition problem for group rings. 相似文献
68.
Frédérique Bassino Armando Martino Cyril Nicaud Enric Ventura Pascal Weil 《Random Structures and Algorithms》2013,42(3):349-373
The usual way to investigate the statistical properties of finitely generated subgroups of free groups, and of finite presentations of groups, is based on the so‐called word‐based distribution: subgroups are generated (finite presentations are determined) by randomly chosen k ‐tuples of reduced words, whose maximal length is allowed to tend to infinity. In this paper we adopt a different, though equally natural point of view: we investigate the statistical properties of the same objects, but with respect to the so‐called graph‐based distribution, recently introduced by Bassino, Nicaud and Weil. Here, subgroups (and finite presentations) are determined by randomly chosen Stallings graphs whose number of vertices tends to infinity. Our results show that these two distributions behave quite differently from each other, shedding a new light on which properties of finitely generated subgroups can be considered frequent or rare. For example, we show that malnormal subgroups of a free group are negligible in the graph‐based distribution, while they are exponentially generic in the word‐based distribution. Quite surprisingly, a random finite presentation generically presents the trivial group in this new distribution, while in the classical one it is known to generically present an infinite hyperbolic group. © 2012 Wiley Periodicals, Inc. Random Struct. Alg., 2013 相似文献
69.
70.
Brent Kerby 《代数通讯》2013,41(12):5087-5103
In 1993, Muzychuk [23] showed that the rational Schur rings over a cyclic group Z n are in one-to-one correspondence with sublattices of the divisor lattice of n, or equivalently, with sublattices of the lattice of subgroups of Z n . This can easily be extended to show that for any finite group G, sublattices of the lattice of characteristic subgroups of G give rise to rational Schur rings over G in a natural way. Our main result is that any finite group may be represented as the (algebraic) automorphism group of such a rational Schur ring over an abelian p-group, for any odd prime p. In contrast, over a cyclic group the automorphism group of any Schur ring is abelian. We also prove a converse to the well-known result of Muzychuk [24] that two Schur rings over a cyclic group are isomorphic if and only if they coincide; namely, we show that over a group which is not cyclic, there always exist distinct isomorphic Schur rings. 相似文献