** the exceptional and twisted groups of Lie type ( including the Tits group ).

*: The Tits group is generally considered of this form, though strictly speaking it is not of Lie type, but rather index 2 in a group of Lie type.

* Tits group, named after Jacques Tits

Tits demonstrated how to every such group G one can associate a simplicial complex Δ = Δ ( G ) with an action of G, called the spherical building of G. The group G imposes very strong combinatorial regularity conditions on the complexes Δ that can arise in this fashion.

Tits proved a remarkable theorem: all spherical buildings of rank at least three are connected with a group ; moreover, if a building of rank at least two is connected with a group then the group is essentially determined by the building.

If a group G acts simplicially on a building X, transitively on pairs of chambers C and apartments A containing them, then the stabilisers of such a pair define a BN pair or Tits system.

Tits proved that all irreducible spherical buildings ( i. e. with finite Weyl group ) of rank greater than 2 are associated to simple algebraic or classical groups.

Tits also proved that every time a building is described by a BN pair in a group, then in almost all cases the automorphisms of the building correspond to automorphisms of the group ( see ).

The results of Tits on determination of a group by its building have deep connections with rigidity theorems of George Mostow and Grigory Margulis, and with Margulis arithmeticity.

In her spare time she was briefly a backing singer along with friend Lindsay Forrest in the Leeds-based pop group Dawn Chorus and the Blue Tits, fronted by radio DJ Liz Kershaw during the early 1980s.

Sometimes ( such as by John Conway ) the Tits group is regarded as a sporadic group ( because it is not strictly a group of Lie type ), in which case there are 27 sporadic groups.

* Tits group T

* There are 27 sporadic groups, if the Tits group is included.

In mathematics, the Tits group < sup > 2 </ sup > F < sub > 4 </ sub >( 2 )′ is a finite simple group of order 17971200 = 2 < sup > 11 </ sup > · 3 < sup > 3 </ sup > · 5 < sup > 2 </ sup > · 13 found by.

The group < sup > 2 </ sup > F < sub > 4 </ sub >( 2 ) is a group of Lie type and has a BN pair, but the Tits group itself does not have a BN pair.

Plumage characteristics include the lack of a pale wing panel ( formed by pale edges to the secondary feathers in the Willow Tit ), the Marsh Tit's glossier black cap and smaller black ' bib ', although none of these is ' completely reliable '; for example, juvenile Marsh Tits can show a pale wing panel.

Marsh Tits breed mostly in lowland areas, but can reach altitudes of up to 1, 300 m. They prefer large areas of moist, broadleaved woodland, often oak or beech, though they can occupy wet alder woodland, riverside trees, parks and gardens or orchards.

Iwahori – Matsumoto, Borel – Tits and Bruhat – Tits demonstrated that in analogy with Tits ' construction of spherical buildings, affine buildings can also be constructed from certain groups, namely, reductive algebraic groups over a local non-Archimedean field.

This can be seen systematically using a construction known as the magic square, due to Hans Freudenthal and Jacques Tits.

In woodland, Eurasian Sparrowhawks account for the deaths of a third of all young Great Tits ; the two alarm calls given by Great Tits when mobbing a predator, and when fleeing from a nearby hawk, are within the optimum hearing range of both prey and predator ; however, the high-pitched alarm call given when a distant flying Eurasian Sparrowhawk is seen " can only be heard well by the tit.

This can be seen systematically using a construction known as the magic square, due to Hans Freudenthal and Jacques Tits.

Moreover, the exceptions, the sporadic groups, share many properties with the finite groups of Lie type, and in particular, can be constructed and characterized based on their geometry in the sense of Tits.

Variations in the exploratory behaviour of Great Tits ( Parus major ) have been found to be linked with a gene orthologous to the human gene DRD4 ( Dopamine receptor D4 ) which is known to be associated with novelty-seeking behaviour.

Research published in 2007 found that Blue Tits on the eastern Canary Islands of Fuerteventura and Lanzarote are indistinguishable from those in North Africa and so the subspsecies degener should be regarded as a synonym of ultramarinus.

Blue Tits are known to be host to feather mites, and rarely lice and flat flies.

Other than those species formerly considered to be subspecies, the Great Tit's closest relatives are the White-naped and Green-backed Tits of southern Asia.

Russo claims that the name " Total Nonstop Action " came from him and that the original concept was, as they were exclusive to pay per view, to be an edgier product than WWE ; the initials of the company " TNA " being a play on " T & A ", short for " Tits and Ass ".

" Nonetheless, neither the band nor the album proved to be a big commercial success in the US: major chain store Wal-Mart refused to stock it, claiming on its website that it contained " a snarling, swaggering attack on conservatism " in the form of the song " Tits on the Radio ".

The title of the fake cover was Tits ' n Bums, which purported to be a church magazine with articles such as " Are you still a verger?

Moreover, as in the case of compact simple Lie groups, the corresponding groups turned out to be almost simple as abstract groups ( Tits simplicity theorem ).

Tits later reworked the foundational aspects of the theory of buildings using the notion of a chamber system, encoding the building solely in terms of adjacency properties of simplices of maximal dimension ; this leads to simplifications in both spherical and affine cases.

For finitely generated linear groups, however, the von Neumann conjecture is true by the Tits alternative: every subgroup of GL ( n, k ) with k a field either has a normal solvable subgroup of finite index ( and therefore is amenable ) or contains the free group on two generators.

The remaining groups of Lie type were produced by Steinberg, Tits, and Herzig ( who produced < sup > 3 </ sup > D < sub > 4 </ sub >( q ) and < sup > 2 </ sup > E < sub > 6 </ sub >( q )) and by Suzuki and Ree ( the Suzuki – Ree groups ).

* Ke, Dianhua & Lu, Xin ( 2009 ): Burrow use by Tibetan Ground Tits Pseudopodoces humilis: coping with life at high altitudes.

Data from 157 woodlands covered by the RSPB / BTO Repeat Woodland Bird Survey showed that the abundance of Marsh Tits in 2003-2004 corresponded with the vegetation present 2 – 4 metres above the ground, the shrub layer.

The study concluded that damage to the shrub layer, caused by overgrazing by deer, for example, may make woodland less suitable for Marsh Tits.

The hidden seeds are prone to being stolen, by other Marsh Tits or other species, so birds often fly from one site to another before deciding on a hiding place.

A study in Bourton Woods, Gloucestershire, England, found that nestboxes were used by Marsh Tits in successive years in only 20 % of cases.

The prison officers, or " screws " as they are called by the women, comprised the firm but fair governor Erica Davidson ( Patsy King ), flanked by the diametrically opposed dour Deputy governor Vera Bennett ( Fiona Spence ), dubbed " Vinegar Tits " by the inmates, and compassionate senior officer Meg Jackson ( Elspeth Ballantyne ).

Great Tits are primarily insectivorous in the summer, feeding on insects and spiders which they capture by foliage gleaning.

A study published in 2007 found that Great Tits helped to reduce caterpillar damage in apple orchards by as much as 50 %.

The nests of Great Tits are raided by Great Spotted Woodpeckers, particularly when nesting in certain types of nest boxes.

Initially introduced by Jacques Tits as a means to understand the structure of exceptional groups of Lie type, the theory has also been used to study the geometry and topology of homogeneous spaces of p-adic Lie groups and their discrete subgroups of symmetries, in the same way that trees have been used to study free groups.

The notion of a building was invented by Jacques Tits as a means of describing simple algebraic groups over an arbitrary field.