* In elementary arithmetic, the set of integers, Z, considered as a group under addition, has a unique nontrivial automorphism: negation.

Xylenol has two methyl groups in addition to the hydroxyl group, and, for this structure, 6 isomers exist.

; Metropolitan bishop: A metropolitan bishop is an archbishop in charge of an ecclesiastical province, or group of dioceses, and in addition to having immediate jurisdiction over his own archdiocese, also exercises some oversight over the other dioceses within that province.

The group that finally overthrew President Patassé consisted of – in addition to Bozizé's own rebels – 100 soldiers from Chad's Military.

In addition, other assaults, robbery, tiger kidnapping, extortion, fuel laundering and smuggling were undertaken by the group.

In addition to igniting spontaneously in air, it reacts explosively with water even at low temperatures, more so than other members of the first group of the periodic table.

If the addition of a functional group takes place at the less substituted carbon atom of the double bond, then the electrophilic substitution with acids is not possible.

While the addition to the electron-rich alkenes and alkynes is mainly electrophilic, the nucleophilic addition plays an important role for the carbon-heteroatom multiple bonds, and especially its most important representative, the carbonyl group.

During his recovery from a heart attack late in 1955, he huddled with his closest advisors to evaluate the GOP's potential candidates ; the group, in addition to his doctor, concluded a second term was well advised, and he announced in February 1956 he would run again.

These age groups roughly correspond to those standardized by FINA, with the addition of a youngest age group for divers 9 and younger, Group E, which does not compete nationally and does not have a tower event ( although divers of this age may choose to compete in Group D ).

This led to the addition of the number sign (#, sometimes called ' octothorpe ,' ' pound ' or ' diamond ' in this context-' hash ' or ' gate ' in the UK ) and asterisk or " star " (*) keys as well as a group of keys for menu selection: A, B, C and D. In the end, the lettered keys were dropped from most phones, and it was many years before these keys became widely used for vertical service codes such as * 67 in the United States of America and Canada to suppress caller ID.

* If we think of as the group of real numbers under addition, then the direct product still consists of.

Additive notation is typically used when numerical addition or a commutative operation other than multiplication interprets the group operation ;

Intuitively, a field is a set F that is a commutative group with respect to two compatible operations, addition and multiplication, with " compatible " being formalized by distributivity, and the caveat that the additive identity ( 0 ) has no multiplicative inverse ( one cannot divide by 0 ).

The most common way to formalize this is by defining a field as a set together with two operations, usually called addition and multiplication, and denoted by + and ·, respectively, such that the following axioms hold ; subtraction and division are defined implicitly in terms of the inverse operations of addition and multiplication :< ref group =" note "> That is, the axiom for addition only assumes a binary operation The axiom of inverse allows one to define a unary operation that sends an element to its negative ( its additive inverse ); this is not taken as given, but is implicitly defined in terms of addition as " is the unique b such that ", " implicitly " because it is defined in terms of solving an equation — and one then defines the binary operation of subtraction, also denoted by "−", as in terms of addition and additive inverse.

Her personal letters to leaders of the Revolution influenced policy ; in addition, she often hosted political gatherings of the Brissotins, a political group which allowed women to join.

For example, the cyclic group of addition modulo n can be obtained from the integers by identifying elements that differ by a multiple of n and defining a group structure that operates on each such class ( known as a congruence class ) as a single entity.

In addition, Hayek attracted an exceptionally able group of students who were dedicated to a libertarian ideology.

In addition to his cosmological writings, Bruno also wrote extensively on the art of memory, a loosely organized group of mnemonic techniques and principles.

In addition, land has been purchased to permit doubling the size of the plant in the future.

In addition, the size distribution obtained from visual and radar observations of meteors may be extrapolated to the micrometeorite domain.

These operations are compounding ( or the addition of one idea onto another, such as a horn on a horse to create a unicorn ); transposing ( or the substitution of one part of a thing with the part from another, such as with the body of a man upon a horse to make a centaur ); augmenting ( as with the case of a giant, whose size has been augmented ); and diminishing ( as with Lilliputians, whose size has been diminished ).

In addition, the strict enforcement of new rules governing the size, shape and construction of the ball caused it to travel

Upon his death, he left a country doubled in size ( mostly through the addition of land in today's Ukraine, then the Duchy of Halicz ), prosperous, wealthy and with great prospects for the future.

In addition to these critical items, the equipment used to assemble the cartridge also has an effect on its uniformity / consistency and optimal shape / size ; dies used to size the cartridges can be matched to the chamber of a given gun.

In addition, ordinary matter is not strong enough to support a hollow shape of planetary size against the force of gravity ; a planet-sized hollow shell with the known, observed thickness of the Earth's crust, would not be able to achieve hydrostatic equilibrium with its own mass and would collapse.

In addition, since ISO 9660 works by segmenting the CD-ROM into logical blocks, the size of these blocks is found in the primary volume descriptor as well.

The Libro de Juegos offers such evidence in the difference in size between the half-and full-page illustrations in addition to changes in framing techniques amongst the folios: geometrical frames with embellished corners, architectural frames established by loosely perspectival rooftops and colonnades, and games played under tents.

In addition, technological changes prior to the merger movement within companies increased the efficient size of plants with capital intensive assembly lines allowing for economies of scale.

In addition, the relatively small size of the penicillin molecule allows it to penetrate deeply into the cell wall, affecting its entire depth.

In 1994 the centre was expanded again, tripling in size and a decade later it was further expanded by the addition of the Wolfson Wing.

In addition to describing the qualities of the different types of wood and their suitability for shipbuilding, the Yukti Kalpa Taru gives an elaborate classification of ships based on their size.

In addition, the government considered reducing the size of the army by 100, 000, although this plan was shelved.

In addition to the variety of flavors, Spam is sold in tins smaller than the twelve-ounce standard size.

The majority of the palace buildings are quadrangular in plan, with all the rooms opening on to a central court ; and the whole reached its present size simply by the gradual addition of new quadrangles, designed on the same principle, though varying in dimensions, and connected with each other by smaller rooms and passages.

In addition for use as an internal combustion engine, the basic Wankel design has also been used for gas compressors, and superchargers for internal combustion engines, but in these cases, although the design still offers advantages in reliability, the basic advantages of the Wankel in size and weight over the four-stroke internal combustion engine are irrelevant.

** The addition of a new section of the Outer City fortifications is completed in southern Beijing, bringing the overall size of Beijing to 18 square miles ( 4662 hectares ).

CPUs generally have a way of detecting this to support addition of numbers larger than their register size, typically using a status bit.

In addition to their small size, the surface normal operation of VCSOAs leads to a number of advantages, including low power consumption, low noise figure, polarization insensitive gain, and the ability to fabricate high fill factor two-dimensional arrays on a single semiconductor chip.

In addition to the size of the group, Steve Gillon has suggested that one thing that sets the baby boomers apart from other generational groups is the fact that " almost from the time they were conceived, Boomers were dissected, analyzed, and pitched to by modern marketers, who reinforced a sense of generational distinctiveness.

In addition to placing the most commonly used letters in setting text in a given language in the easiest positions for the typesetter to get to, the characters ' boxes varied in size depending upon the frequency of usage of the character.

In addition, the hypothesis suggests that the increase in temperature would tend to increase the size of the ice crystals in the cirrus cloud, possibly causing the reflection of solar radiation and the reflection of the Earth's infrared radiation to balance out.