# automorphism

share

## Examplesautomorphism's examples

• The argument basically is that a group is the automorphism group of its (colored) Cayley graph and that the colors of edge in the Cayley graph can be coded into an uncolored graph that has the same automorphism group. This argument seems to carry over to the countably infinite case. — “Realizing groups as automorphism groups of graphs. - MathOverflow”,
• This article defines an automorphism property, viz a property of group automorphisms. The concept of class automorphism first took explicit shape when it was observed that there are automorphisms of groups that take each element to within its conjugacy. — “Class automorphism - Groupprops”, groupprops.wiki-
• The exact definition of an automorphism depends on the type of "mathematical object" in question and what, precisely, constitutes an "isomorphism" of that object. The most general setting in which these words have meaning is an abstract branch of mathematics called [[category theory]. — “Automorphism”,
• of a division ring with an anti-automorphism but no involution gives examples of division algebras over Q which have an anti-automorphism but no involution, as. — “DIVISION ALGEBRAS WITH AN ANTI-AUTOMORPHISM BUT WITH NO”, csun.edu
• We show that certain ﬁnite groups do not arise as the automorphism The automorphism group of a 2-generated. free algebra also has a distinguished involution, namely the automorphism induced by. — “AUTOMORPHISM GROUPS OF SQUARES AND OF FREE ALGEBRAS”, spot.colorado.edu
• automorphism ( ¦ödō′mör′fizəm ) ( mathematics ) An isomorphism of an algebraic structure with. — “Automorphism: Definition from ”,
• This article defines an automorphism property, viz a property of group automorphisms. An automorphism of a group is termed an inner automorphism if it can be expressed as conjugation by an element of the group. — “Inner automorphism - Groupprops”,
• Then the Frobenius automorphism is the automorphism defined by the formula for all , where (the cardinality of ) Then the Frobenius automorphism of the extension of residue fields can be uniquely lifted to an automorphism , called the Frobenius automorphism of the unramified. — “Springer Online Reference Works”,
• Definition of automorphism in the Online Dictionary. Meaning of automorphism. Pronunciation of automorphism. Translations of automorphism. automorphism synonyms, automorphism antonyms. Information about automorphism in the free online English. — “automorphism - definition of automorphism by the Free Online”,
• No relations. Automorphism Group—Aut(G) Isomorphism φ : G G. Group under composition Free Group Automorphism Representations v0.3. Intro. Groups of Interest. — “Representations of Automorphism Groups of Free Groups”, math.byu.edu
• It is easy to show the conjugation map is in fact, a group automorphism. An automorphism that isn't inner is called an outer automorphism. — “PlanetMath: inner automorphism”,
• A field automorphism fixes the smallest field containing 1, which is , the rational numbers, in the case of field characteristic zero. The set of automorphisms of which fix a smaller field forms a group, by composition, called the Galois group, written. — “Field Automorphism -- from Wolfram MathWorld”,
• automorphism (plural automorphisms) (mathematics) An isomorphism of a mathematical object Automorphism on Wikipedia.Wikipedia. Automorphism in the 1911 Encyclopædia Britannica. — “automorphism - Wiktionary”,
• Automorphism brings nothing that Eiffel doesn't already have Before I elaborate on the changes in the language to support automorphism, we need to make sure that it can actually be implemented, and what. — “Automorphism | eiffelroom”,
• In field theory, a field automorphism is an automorphism of the algebraic structure of a field, that is, a bijective function from the field onto itself which respects the fields operations of addition and multiplication. The automorphisms of a given field K form a group, the automorphism group. — “Field automorphism - encyclopedia article - Citizendium”,
• The inner automorphism corresponding to g is also called the An automorphism on a group is said to lift or extend an automorphism on a subgroup. — “EXTENSIBLE AUTOMORPHISMS: A POSSIBLE APPROACH”, cmi.ac.in
• Finding a canonical labeling of a graph reveals its automorphism group. computing the automorphism group of G+v. If some groups could not delete to the automorphism. group of G, then they certainly cannot appear as the automorphism group of G+v which may allow. — “Automorphism groups of a graph and a vertex-deleted subgraph”, math.unl.edu
• An automorphism preserves the structural properties of a group, e.g. The composition of two automorphisms is again an automorphism, and with composition as binary operation the set of all automorphisms of a group G,. — “Automorphism - Online Dictionary of Crystallography”,
• In addition to the usual properties of GrpAuto (such as Order, Ngens, etc.), two special fields, GenWeights and WeightSubgroupOrders, are provided for automorphism groups of (non p-group) pc-groups. These each relate to weight subgroups of the automorphism group. — “Automorphism Group”, umich.edu
• In mathematics, an automorphism is an isomorphism from a mathematical object to itself. The exact definition of an automorphism depends on the type of "mathematical object" in question and what, precisely, constitutes an "isomorphism". — “Automorphism - Wikipedia, the free encyclopedia”,

## Blogs & Forumblogs and forums about automorphism

• “ show that the only addition-and-multiplication-preserving automorphism is the identity, but it's been a long But there is an interesting automorphism of the complex numbers; it has f(a + bi) = a - bi for all real a and”
— The Universe of Discourse : Imaginary units, again,

• “Subject: Codes automorphism groups. Dear Colleagues, I would like to compute codes automorphism groups. and some related ones. I did not find a direct. way to do it by GAP. Perhaps, somebody of GAP - users. have an experience in such computations and can help me. Many thanks in advance. Best regards,”
— GAP Forum: Codes automorphism groups, www-gap.dcs.st-

• “Thu Mar 30 11:50:59 BST 2006. Previous message: [GAP Forum] Experimental GAP Installer for Windows. Next message: [GAP Forum] From: Willem De Graaf Subject: Re: [GAP Forum] Automorphism of Algebra To: Alper Odaba?”
— [degraaf@science.unitn.it: Re: [GAP Forum] Automorphism of, mail.gap-

• “Prove that every group with more than two elements has a non-trivial automorphism. identity over the quotient group is a nontrivial automorphism of the”
— Tanya Khovanova's Math Blog " Blog Archive " An Organic Puzzle,

• “(1) Finding symmetries of a formula is a subcase of the coloured graph automorphism problem. (2) As n goes to infinity, the probability that a random propositional formula has a trivial automorphism group tends to 1”
— That Logic Blog: New Blog on the Spot,

• “qt python boost sip symmetry permutation automorphism stereochemistry cheminformatics by 1 posted to Tim Vandermeersch's chemical blog on Wed 16th Sep 09”
— Chemical blogspace - Blog details,

• “Forum. Contact. LAN Parties. Microsoft Game Camp. Log in | Register | Search | Memberlist | Usergroups | FAQ | Viewing profile :: automorphism Computer Club Forum Index. Jump to: Copyright © 2007 University of Ottawa Computer Club”
— University of Ottawa Computer Club ~ Viewing profile,