[PDF] Top 20 Generation problems for finite groups

... of groups that do and do not have property B we sought to high- light how rare groups with property B ...dihedral groups, showing that all dihedral groups of order 2p n have prop- erty B, for ... See full document

... a finite d-generated group with high probability which are significantly tighter than the ones obtained in the paper of Jaikin-Zapirain and Pyber (Random generation of finite and profinite ... See full document

... some problems to considering groups over ...arithmetic groups see ...to groups defined over Q ...automorphism groups of positive definite quadratic Z -lattices under totally real scalar ... See full document

... decision problems in group theory, and it is known that the problem is undecidable for many classes of groups (see Chandler and Magnus, ...polycyclic-by-finite groups, however, is a subclass ... See full document

... In [29], Wamsley states that for any nilpotent group G, abdef(G) = def(G). He also poses several questions relating to the efficiency of nilpotent groups. He asks whether a p-group is necessarily efficient, ... See full document

... This concept actually first arose in the context of field arithmetic. Various theorems that are valid for “almost all” k-tuples in the absolute Galois group G(F ) of a field F appear in [6]. Answering a question of Fried ... See full document

... of finite subgroups in locally finite, simple groups or LFS-groups as we will call ...open problems about centralizers of subgroups in LFS-groups and applications of the known ... See full document

... simple groups (see [2]). Since then, several authors have shown the conjecture to hold for certain groups. The following characterization in terms of irreducible characters can be used to check the ... See full document

... CHAPTER TWO: SYMMETRIC REPRESENTATION OF L 2(ll) ELEMENTS Introduction ... 25[r] ... See full document

... when finite) is a group generated by an involution and an element of order 3, whose product has order ...Such groups have been studied intensively, starting from the pioneering works of Hurwitz [7] and ... See full document

... Further, the above theorem was used by the authors in [19] to classify all the nonabelian p-groups of order p 4 (p an odd prime) which have a Johnson polynomial. The purpose of this article is to examine the ... See full document

... Sylow subgroups of 3-BCI-groups are classified in [8] and the nilpotent 3-BCI-groups are determined in [10]. Also in [9], the isomorphisms of connected bi-Cayley graphs of cyclic groups, with valency ... See full document

... metacyclic groups is closely related to the class of Q -admissible groups: a group G is said to be Q -admissible if there exists a Q -central division algebra containing a maximal subfield K such that G(K/ ... See full document

... Theorem . Let F be a saturated formation containing all supersoluble groups. A group G ∈ F if and only if there exists a normal subgroup E of G such that G/E ∈ F and for every non-cyclic Sylow subgroup P of F * ... See full document

... 15] groups with property B, that is groups G with ig(G) = sg(G), were ...also groups with the basis property, that is groups such that all its subgroups have property B, hence have ... See full document

... Observe that n ≤ | X | + ( | X 2 | − | X | ) + . . . + ( | X n | − | X n − 1 | ) = | X n | ≤ | G | hence | X | G | | = | X n | . Since 1 ∈ X | G | , X | G | ⊆ X 2 | G | and from | X | G | | = | X n | = | X 2 | G | | we ... See full document

... We briefly review the history of this result. G. Miller [17], and later and independently Philip Hall in [4], asked whether the condition Π ( P ) = G for every complete Sylow sequence P of G implies the solvability of G ... See full document

... group G. This probability is a useful formula to determine how close a subset is to be a subgroup of G. In (Abd Rhani et al., 2016), some upper and lower bounds of this probability are found, when the groups are ... See full document

... of groups. The study of permutation groups, which is the basic class of groups, leads to abstract groups that can be described in a presentation by the group generators and some suitable ...of ... See full document

... In this section we will list some basic results which will be needed in later parts of this paper. The paper [8] considered the following notion “weaker” than conjugacy expansiveness. We say that G is normal conjugacy ... See full document