Every finitely presented group G has a quotient group with solvable word problem – namely the trivial group. We will construct a finitely presented group G such that every non-trivial quotient of G has unsolvable word problem (of degree 0′ in case the quotient is recursively presented) and such that every countable group is embedded in some quotient of G. A presentation of a group is an ordered...

1 13 4. Free rational curves 14 5. Uniruledness 16 5.1. Definitions equivalent to uniruledness 16 5.2. Examples and consequences of uniruledness 18 6. Rational connectivity 20 6.1. Definitions equivalent to rational connectivity 21 6.2. Rational chain-connectivity implies rational connectivity 22 6.3. Examples and consequences of rational connectivity 26 7. The MRC quotient 27 7.1. Quotients by...

In this paper we introduce a new definition of the first non-abelian cohomology of topological groups.  We relate the cohomology of a normal subgroup $N$ of a topological group $G$ and the quotient $G/N$ to the cohomology of $G$. We get the inflation-restriction exact sequence. Also, we obtain a seven-term exact cohomology sequence up to dimension 2. We give an interpretation of the first non-a...

Uji Kompetensi Mahasiswa Program Profesi Dokter (UKMPPD) merupakan suatu exit exam bagi mahasiswa yang telah menjalani seluruh proses pembelajaran dan sebelum sumpah dokter, mana dapat menjadikanya cemas. Gangguan cemas, depresi, stres masalah kejiwaan terbanyak dihadapi kedokteran. Sebanyak 71,9% kedokteran mengalami stres. Stres pada UKMPPD disebut akademik karena bersumber tuntutan akademik....

We describe hypergeometric functions of Deligne-Mostow type for open subsets of the configuration space of six points on P, induced from those for seven points on P. The seven point ball quotient example DM(2, 1) does not appear on Mostow’s original list [9], but does appear on Thurston’s corrected version [12]. We show that DM(2, 1) is a finite cover of the moduli space of cubic surfaces MC en...

When N is a normal subgroup of G, can we reconstruct G from N and G/N? In general, no. For instance, the groups Z/(p2) and Z/(p) × Z/(p) (for prime p) are nonisomorphic, but each has a cyclic subgroup of order p and the quotient by it also has order p. As another example, the nonisomorphic groups Z/(2p) and Dp (for odd prime p) have a normal subgroup that is cyclic of order p, whose quotient is...

The main result is that the fundamental groupoid of the orbit space of a discontinuous action of a discrete group on a Hausdorff space which admits a universal cover is the orbit groupoid of the fundamental groupoid of the space. We also describe work of Higgins and of Taylor which makes this result usable for calculations. As an example, we compute the fundamental group of the symmetric square...

In this paper, in addition to some elementary facts about the ultra-groups, which their structure based on the properties of the transversal of a subgroup of a group, we focus on the relation between a group and an ultra-group. It is verified that every group is an ultra-group, but the converse is not true generally. We present the conditions under which, for every normal subultra-group of an u...

abstract. in this paper we study some relations between the power andquotient power graph of a finite group. these interesting relations motivateus to find some graph theoretical properties of the quotient power graphand the proper quotient power graph of a finite group g. in addition, weclassify those groups whose quotient (proper quotient) power graphs areisomorphic to trees or paths.