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Simple machines
\"Describes how simple machines are used in construction and how they make work easier. Includes experiments\"--Provided by publisher.
Book
Automorphism Orbits and Element Orders in Finite Groups: Almost-Solubility and the Monster
For a finite group
eBook
Simple machines
\"Machines help make work easier, like when you need to lift something heavy or reach way up high. There are six simple machines: the lever, the wheel and axle, the pulley, the ramp, the wedge, and the screw. Can you adjust a seesaw to lift an elephant? What happens when you combine two or more simple machines? Read and find out!\"--Amazon.com.
Book
Regular subgroups of primitive permutation groups
The authors address the classical problem of determining finite primitive permutation groups G with a regular subgroup B. The main theorem solves the problem completely under the assumption that G is almost simple. While there are many examples of regular subgroups of small degrees, the list is rather short (just four infinite families) if the degree is assumed to be large enough, for example at least 30!. Another result determines all primitive groups having a regular subgroup which is almost simple. This has an application to the theory of Cayley graphs of simple groups.
eBook
Simple machines : inventions that changed the world--and the science behind them
Leo teaches his cat Pallas all about simple machines by applying his knowledge of science to their stone age world. Engaging illustrations and stories provide a fun introduction to science concepts, including wheel and axles, levers, pulleys, wedges, screws, and more. Information boxes accompany each story to explore real applications of simple machines in the natural and designed world.
Book
Factorizations of Almost Simple Groups with a Solvable Factor, and Cayley Graphs of Solvable Groups
A characterization is given for the factorizations of almost simple groups with a solvable factor. It turns out that there are only
several infinite families of these nontrivial factorizations, and an almost simple group with such a factorization cannot have socle
exceptional Lie type or orthogonal of minus type. The characterization is then applied to study
eBook
Wedges at work
\"Describes wedges, including the history, function, and everyday uses.\"-- Provided by publisher.
Book
Cohomological Tensor Functors on Representations of the General Linear Supergroup
We define and study cohomological tensor functors from the category
eBook
Curious Pearl tinkers with simple machines : an augmented reading science experience
\"Curious Pearl and her brother don't like chores. They'd rather play with their kitten. But Dad looks serious, so Pearl and her brother come up with a solution. They build a contraption to help them with their chores. As they build, Pearl teaches her brother all about simple machines. Free bonus video content through the Capstone 4D augmented reality app enhances the science experience.\"-- Provided by publisher.
Book
On Fusion Systems of Component Type
This memoir begins a program to classify a large subclass of the class of simple saturated 2-fusion systems of component type. Such a
classification would be of great interest in its own right, but in addition it should lead to a significant simplification of the proof
of the theorem classifying the finite simple groups.
Why should such a simplification be possible? Part of the answer lies in the
fact that there are advantages to be gained by working with fusion systems rather than groups. In particular one can hope to avoid a
proof of the B-Conjecture, a important but difficult result in finite group theory, established only with great effort.
But in
addition, the program involves a reorganization of the treatment of “groups of component type”, or perhaps more accurately, of “fusion
systems of component type”. The groups of component type should be viewed as “odd” groups, in that most examples are groups of Lie type
over fields of odd order. The remaining simple groups should be viewed as “even” groups, since most of the examples in this class are of
Lie type over fields of even order. There are corresponding notions of “odd” and “even” 2-fusion systems.
In our program the
class of odd groups, and/or fusion systems, is contracted in a carefully chosen manner, so as to avoid difficulties associated to
certain “standard form problems”. This has the effect of greatly simplifying the treatment of the odd 2-fusion systems, and then also
the treatment of the odd simple groups. Of course the flip side of such a reorganization is to enlarge the class of even objects, so
that the approach may make it more difficult to treat that class. But it is our sense that the trade off should lead to a net
simplification.
This change in the partition of simple groups into odd and even groups is not dissimilar to the one in the
program of Gorenstein, Lyons, and Solomon (hereafter referred to as GLS) to rewrite the proof of the classification.
In the
introduction, we expand upon these themes, making them a bit more precise, supplying some background, and eventually stating some of our
major theorems. Then in the body of the paper, we fill in details and begin the actual program.
eBook