Weeping in Modern Jihadi Groups

Content Analysis of Jihadi Extremist Groups' Videos

This paper presents an exploratory study of jihadi extremist groups’ videos using content analysis and a multimedia coding tool to explore the types of videos, groups’ modus operandi, and production features. The videos convey messages powerful enough to mobilize members, sympathizers, and even new recruits to launch attacks that will once again be captured and disseminated via the Internet. Th...

Understanding Jihadi Networks

The terrorist threat to the United States of America comes from a violent Islamist revivalist social movement, united by a utopian vision of justice and fairness. Our efforts to deal with this threat are hampered by the wide variety of commonly held beliefs about terrorism. Conventional wisdom offers up several explanations: terrorists are a product of poverty and broken families; ignorance; th...

18.703 Modern Algebra, Quotient Groups

Given a group G and a subgroup H, under what circumstances can we find a homomorphism φ : G −→ G', such that H is the kernel of φ? Clearly a necessary condition is that H is normal in G. Somewhat surprisingly this trivially necessary condition is also in fact sufficient. The idea is as follows. Given G and H there is an obvious map of sets, where H is the inverse image of a point. We just put X...

18.703 Modern Algebra, Cyclic Groups

18.703 Modern Algebra, Permutation groups

Proof. (5.2) implies that the set of permutations is closed under com­ position of functions. We check the three axioms for a group. We already proved that composition of functions is associative. Let i : S −→ S be the identity function from S to S. Let f be a permutation of S. Clearly f ◦ i = i ◦ f = f . Thus i acts as an identity. Let f be a permutation of S. Then the inverse g of f is a perm...