* 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, our way of dealing directly with natural phenomena has also changed.

Besides showing no inclination, apparently, to absent himself from his native region even for short periods, and in addition writing a shelf of books set in the region, he has handled in those books an astonishingly complete list of matters which have been important in the South during the past hundred years.

In San Francisco he has worked with Brew Moore, Charlie Mingus, and other `` swinging '' musicians of secure reputation, thus placing himself within established jazz traditions, in addition to being a part of the San Francisco `` School ''.

In addition, he said, he has answered more than 400 messages of congratulations which led him to the comment that he himself had decided he wouldn't send another congratulatory message for the rest of his life.

In addition, the motor has the seal of approval of the Underwriters Laboratories, which means it is safe.

Thus, there has come into being a situation in which the state must raise all of its own revenues and, in addition, must give assistance to its local governments.

In addition to the basic programs in wavelength standards, spectroscopy, solid state physics, interactions of the free electron and atomic constants which are necessary to provide the foundation for technological progress, the Bureau has strengthened its activities in laboratory astrophysics.

In addition, petitioner has failed to show any particular need for the report and notes.

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

In addition to these rules, Carleton has added the following: 1.

In addition, little work has been done on a comparative basis in regard to the normal existence of bronchial artery-pulmonary artery anastomoses.

In addition, this country has been settled by many peoples of many heritages and their lore has become acculturated slowly, in an age of print and easy communication, within an ever-expanding and changing society.

In addition, Dr. Clark has studied at Rhode Island State College and Massachusetts Institute of Technology.

In addition to the interlibrary loan service and the children's program, headquarters has a public relations director who seeks to get wider grassroots support for quality library service in the county ; ;

For this latest addition to the Great Letters Series, under the general editorship of Louis Kronenberger, Miss Hardwick has made a selection which admirably displays the variety of James's genius, not to mention the felicities of his style.

In addition, mixed race ( European and African ) people amount to about 2 %, with a small ( 1 %) population of whites, mainly ethnically Portuguese ( as a former overseas territory of Portugal until 1975, the Portuguese make up currently the largest non-African population, with certainly more than 100, 000, a number that has been constantly increasing from the 2000s, because of Angola's growing demand for qualified human resources.

Roughly 26 % are followers of traditional forms of Protestantism ( Congregationals, Methodists, Baptista, Lutherans, Reformed ), but over the last decades there has in addition been a growth of Pentecostal communities and African Initiated Churches.

As per the American Dental Association, regular brushing and proper flossing are enough in most cases although the ADA has placed its Seal of Approval on many mouthwashes containing alcohol ( in addition to regular dental check-ups ).

Since then commercial interest in mouthwashes has been intense and several newer products claim effectiveness in reducing the build-up in dental plaque and the associated severity of gingivitis ( inflammation of the gums ), in addition to fighting bad breath.

In addition to the Conservatory, AFI has a tuition-free program called the AFI Directing Workshop for Women that operates each spring and summer from the Los Angeles campus.

Conium maculatum has been used as a sedative and in treatments for arthritis and asthma in addition to its most famous use: as a “ humane ” method of killing criminals and philosophers.

In addition, Sirius has been played in a variety of TV shows and movies including the episode " Vanishing Act " of The Adventures of Jimmy Neutron: Boy Genius, and the 2009 film Cloudy with a Chance of Meatballs.