[PDF] Top 20 Groups whose locally maximal product free sets are complete

... Suppose the only filled groups of order 2 n−1 are elementary abelian or extraspecial. If n is 2 or 3, then the result holds, so we may assume n ≥ 4. Now G is clearly not cyclic. Moreover, by Lemma 3.3, G is not of ... See full document

... points, maximal by inclusion, with no three ...non-abelian groups, where of course we speak of product-free ...all complete product-free sets are locally ... See full document

... a locally maximal product-free set of size 4, then | G | ≤ ...The locally maximal product-free sets of size 4 in abelian groups of order up to 32 were ... See full document

... of product-free sets in groups of even ...the maximal size of a sum-free set in an arbitrary abelian ...largest product-free set in a group of order n has size at ... See full document

... every product-free set is contained in a locally maximal product-free set, we can gain informa- tion about product-free sets in a group by studying its ... See full document

... the maximal q congruence contained in ...a complete modu- lar lattice isomorphism between q normal subpartial groups of S and q congruence on S, which is analogous to the classical result (see, ... See full document

... sum-free sets in the integers (for example [2, 3]) and the density and number of sum-free sets in abelian groups (for example ...sum-free sets are also closely related to ... See full document

... We have shown our results as above and given examples of constructed graphs in Figure 1 & 2. The main result from our study has been expressed in lemma 1. Lemma 1 shows that in determining the number of graphs ... See full document

... all locally maximal product-free sets of size 3 occurring in groups of order up to 24 (in fact, up to 37 in the original ...all locally maximal ... See full document

... finite groups containing locally maximal sum-free set of size 1 (see [6, Theorem ...of locally maximal sum-free set S satisfying | √ S | > 2 | S | , we show that such ... See full document

... sum-free sets which are not locally ...understand locally maximal sum-free sets, Bertram [6, Section 5] asked the following questions: Question ...every locally ... See full document

... The present communication describes a group of mutants whose temperature-sensitive ts gene product is required to initiate, but not to complete, a single round of viral deoxyribonucleic [r] ... See full document

... of locally closed sets was introduced by Bourbaki [3] in 1966 then the authors Ganster and Reilly [6] have studied it ...called locally closed if A = U ∩ F , where U is open and F is ...a ... See full document

... Let ~,K2 be knots whose groups have cohomological Then so does the knot group of the product knot We see that the set of all knots whose groups satisfy our conjecture form a commutative [r] ... See full document

... Proof of Theorem 12. By [23], the class of groups with MCF word problem is closed under free products. We can therefore reduce to connected graphs Γ. The class of groups with MCF word problem is ... See full document

... Clearly, the problem of whether a group given by finite presentation splits as a free product is not solvable for arbitrary finitely presented groups either splits as a free product if a[r] ... See full document

... paper, maximal product of two fuzzy graphs is ...their maximal product is always ...the maximal product of two connected fuzzy graphs is ...the maximal product of ... See full document

... abelian, K/K ′ is elementary abelian and |Z(G)| ̸= 3. But then applying Lemma 2.11(b) shows that K must be abelian which is a contradiction. Therefore K ′ ≰ Z( ¯ G) and so there exists an ¯ s ∈ K ′ \ Z( ¯ G). Let T be a ... See full document

... of whose subgroups are inert is called inertial in [11] where, in the context of gen- eralized soluble groups (with some finiteness conditions), a characterization of inertial groups was ...Inertial ... See full document

... Patients underwent modified radical mastectomy or breast-conserving surgery within four weeks from the last NAC cycle. Patients who did not complete six cycles of NAC received postoperative chemotherapy. For those ... See full document