In this paper we effect a systematic study of transitive subgroups of M24, obtaining 5 transitive maximal subgroups of M24 of which one is primitive and four imprimitive. These results, along with the results of the paper, On subgroups of M2i. I, enable us to enumerate all the maximal subgroups of M24. There are, up to conjugacy, nine of them. The complete list includes one more in addition to ...

background: casein phosphopeptide-amorphous calcium phosphate (cpp-acp) is applied for remineralization of early caries lesions or tooth sensitivity conditions and may affect subsequent resin bonding. this in vitro study investigated the effect of cpp-acp on the shear bond strength of dental adhesives to enamel. materials and methods: sixty extracted human molar teeth were selected and randomly...

Canfield and Mason have conjectured that for all subgroups G of the automorphism group of the Boolean lattice Bn (which can be regarded as the symmetric group Sn) the quotient order Bn/G is a symmetric chain order. We provide a straightforward proof of a generalization of a result of K. K. Jordan: namely, Bn/G is an SCO whenever G is generated by powers of disjoint cycles. In addition, the Bool...

Let G be a finite group and let k be an algebraically closed field of prime characteristic p. Let 5 b e a block of kG, P a /^-subgroup of G and n a /(-element of G. Then the multiplicity of P as a lower defect group of B for the /^-section of n is defined [1, 2, 4] and is denoted by mB(P). We shall prove the following induction theorem for mB(P) in terms of the Brown complex A of chains of non-...

Let Mg,n be the moduli space of Riemann surfaces of genus g with n punctures. From a complex perspective, moduli space is hyperbolic. For example, Mg,n is abundantly populated by immersed holomorphic disks of constant curvature −1 in the Teichmüller (=Kobayashi) metric. When r = dimC Mg,n is greater than one, however, Mg,n carries no complete metric of bounded negative curvature. Instead, Dehn ...

in this paper we study a representation of a fuzzy subgroup $mu$ of a group $g$, as a product of indecomposable fuzzy subgroups called the components of $mu$.  this representation is unique up to the number of components and their isomorphic copies. in the crisp group theory, this is a well-known theorem attributed to remak, krull, and schmidt. we consider the lattice of fuzzy subgroups and som...

The Wiener index is the sum of distances between all pairs of vertices in a connected graph. In this paper, explicit expressions for the expected value of the Wiener index of three types of random pentagonal chains (cf. Figure 1) are obtained.

We show that if G is a stable group of finite weight with no infinite, infinite-index, chains of definable subgroups, then G is superstable of finite U rank. Combined with recent work of Palaćın and Sklinos, we conclude that (Z,+, 0) has no proper stable expansions of finite weight. A corollary of this result is that if P ⊆ Zn is definable in a finite dp-rank expansion of (Z,+, 0), and (Z,+, 0,...

In this paper we describe how the degrees of the irreducible characters of the affine subgroups of the classical groups under consideration can be found inductively. In [4] Gow obtained certain character degrees for all of the affine subgroups of the classical groups. We apply the method of Fischer to the above groups and, in addition to the character degrees given in [4], we obtain some ne...

the subgroups of symplectic groups which fix a non-zero vector of the underlying symplectic space are called affine subgroups., the split extension group $a(4)cong 2^7{:}sp_6(2)$ is the affine subgroup of the symplectic group $sp_8(2)$ of index $255$‎. ‎in this paper‎, ‎we use the technique of the fischer-clifford matrices to construct the character table of the inertia group $2^7{:}o^{-}_{6}(2...