${\rm Aut}(F)\to{\rm Aut}(F/F”)$ is surjective for free group $F$ of rank $\geq 4$

The Free Group of Rank 2 Is a Limit of Thompson’s Group F

From [9], an n-marked group is a pair (G,S) where S is an ordered n-tuple of generators (the n-marking) of the group G. An isomorphism of marked groups must preserve the markings. With Gn the set of all isomorphism classes of n-marked groups, one says that two elements of Gn are no more than e −R apart if they have satisfy the same relations of length no longer than R. This gives a metric on Gn...

A module theoretic approach to‎ ‎zero-divisor graph with respect to (first) dual

Let $M$ be an $R$-module and $0 neq fin M^*={rm Hom}(M,R)$. We associate an undirected graph $gf$ to $M$ in which non-zero elements $x$ and $y$ of $M$ are adjacent provided that $xf(y)=0$ or $yf(x)=0$. Weobserve that over a commutative ring $R$, $gf$ is connected anddiam$(gf)leq 3$. Moreover, if $Gamma (M)$ contains a cycle,then $mbox{gr}(gf)leq 4$. Furthermore if $|gf|geq 1$, then$gf$ is finit...

An Elementary Abelian Group of Rank 4 Is a CI-Group

Let Cay(H, S), S/H be an arbitrary Cayley graph over a finite group H. We shall say that two Cayley graphs Cay(H, S) and Cay(H, T) are Cayley isomorphic if there exists an automorphism . # Aut(H ) such that S=T. It is a trivial observation that two Cayley isomorphic Cayley graphs are isomorphic as graphs. The converse is not true: two Cayley graphs over the same group may be isomorphic as graph...

rflICROCOMPUTER BASED FISH F.~RM PRODUCTION PLANNING

ERCC 4 ( xeroderma pigmentosum , complementation group F )

Xeroderma pigmentosum group F complementing factor; DNA-repair protein complementing XPF cells 905 amino acids; form a stable complex with the ERCC1 protein; The XPF protein and the ERCC1 protein form a complex that exhibits structure specific endonuclease activity that is responsible for the 5' incision during the NER reaction. XPF-ERCC1 also binds to XPA (through ERCC1) and to RPA (through XP...