If a group G has a maximal subgroup H, tl-.en G acts by right multiplication on the set fi of right cosets of H in G as a primitive, but not necessarily faithful, permutation group. As part of the search for new finite simple groups it is of interest to determine all possible groups G, and in particular all simple groups, which contain a given group H as a maximal subgroup. This problem is very...

We provide a complete characterization of all polytopes P ⊆ [0,1]n with empty integer hull whose Gomory-Chvátal rank is n (and, therefore, maximal). In particular, we show that the first GomoryChvátal closure of all these polytopes is identical.

In this paper, we investigate the problems of consensus-making among institution in stock exchange with multiple criteria for evaluating performance when the players (institutions) are supposed to be egoistic and the score for each criterion for a player is supposed to be a positive score. Each player sticks to his superiority regarding the criteria. This paper introduces the models for computi...

In this paper, we prove that any BL-general fuzzy automaton (BL-GFA) and its quotient have the same behavior. In addition, we obtain the minimal quotient BL-GFA and minimal quotient transformation of the BL-GFA, considering the notion of maximal admissible partition. Furthermore, we show that the number of input symbols and time complexity of the minimal quotient transformation of a BL-GFA are ...

Let n n complex matrices P andQ be nontrivial generalized reflection matrices, i.e., P D P D P 1 ¤ In, Q DQ DQ 1 ¤ In. A complex matrix A with order n is said to be a .P;Q/ generalized anti-reflexive matrix, if PAQ D A. We in this paper mainly investigate the .P;Q/ generalized anti-reflexive maximal and minimal rank solutions to the system of matrix equation AX D B . We present necessary and su...

a group g is said to be a (pf)c-group or to have polycyclic-by-finite conjugacy classes, if g/c_{g}(x^{g}) is a polycyclic-by-finite group for all xin g. this is a generalization of the familiar property of being an fc-group. de falco et al. (respectively, de giovanni and trombetti) studied groups whose proper subgroups of infinite rank have finite (respectively, polycyclic) conjugacy classes. ...

We show that the maximal cp-rank of n×n completely positive matrices is attained at a positive-definite matrix on the boundary of the cone of n×n completely positive matrices, thus answering a long standing question. We also show that the maximal cp-rank of 5×5 matrices equals six, which proves the famous Drew-JohnsonLoewy conjecture (1994) for matrices of this order. In addition we present a s...