Any normal subgroup has a corresponding quotient group, formed from the larger group by eliminating the distinction between elements of the subgroup.

* Any topologically closed subgroup of a Lie group is a Lie group.

* Any simply connected solvable Lie group is isomorphic to a closed subgroup of the group of invertible upper triangular matrices of some rank, and any finite dimensional irreducible representation of such a group is 1 dimensional.

* Any simply connected nilpotent Lie group is isomorphic to a closed subgroup of the group of invertible upper triangular matrices with 1's on the diagonal of some rank, and any finite dimensional irreducible representation of such a group is 1 dimensional.

Any symmetry group whose elements have a common fixed point, which is true for all finite symmetry groups and also for the symmetry groups of bounded figures, can be represented as a subgroup of orthogonal group O ( n ) by choosing the origin to be a fixed point.

* Any subgroup of a free group is free.

Any ξ ∈ gives rise to a canonical vertical vector field X < sub > ξ </ sub > by taking the derivative of the right action of the 1-parameter subgroup of H associated to ξ.

Any group scheme G of finite type is an extension of the connected component of the identity ( i. e., the maximal connected subgroup scheme ) by a constant group scheme.

The theorem states: Any linearly ordered abelian group can be embedded as an ordered subgroup of the additive group ℝ < sup > Ω </ sup > endowed with a lexicographical order, where ℝ is the additive group of real numbers ( with its standard order ), and Ω is the set of Archimedean equivalence classes of.

Any Fuchsian group ( a discrete subgroup of SL ( 2, R )) is a Kleinian group, and conversely any Kleinian group preserving the real line ( in its action on the Riemann sphere ) is a Fuchsian group.

Any two components of a group commute, so the layer is a perfect central extension of a product of simple groups, and is the largest normal subgroup of G with this structure.

Any unipotent algebraic group is isomorphic to a closed subgroup of the group of upper triangular matrices with diagonal entries 1, and conversely any such subgroup is unipotent.

Any subgroup of the additive group of a zero ring is an ideal.

* Any dihedral group is metabelian, as it has a cyclic normal subgroup of index 2.

Any neutrons colliding with the helium atoms give an energy signature which can be detected and counted.

Any hydrogen atoms bonded to non-carbon atoms are drawn explicitly.

Any bonds not taken up by halogen atoms are then allocated to hydrogen atoms.

Any atoms off their lattice sites will give visible extra scattering.

( vi ) Any compound, mixture, or preparation which contains any quantity of any of the substances referred to in paragraphs ( b )( 31 )( i ) through ( v ) of this section.

* Carbohydrate – Any compound containing carbon, hydrogen, sometimes oxygen.

Any compound that causes a rise in acetylcholine concentration can potentially overcome BZ-induced inhibition and restore normal functioning ; even the nerve agent VX has been shown to be effective when given under carefully controlled conditions.

Any compound having a catechol structure, like catecholestrogens and catechol-containing flavonoids, are substrates of COMT.

Any type of free-moving compound physics object can demonstrate this problem, but it is especially prone to affecting chain links under high tension and wheeled objects with actively physical bearing surfaces.

Any derivative of quinazoline may be described as a quinazoline compound.

Any alkyl iodide present will give a reaction with the mercury compound to mercury ( II ) iodide which has a red or yellow color.

Any special photographic requirements are also given.

Any tax bill also will revive allegations that some of his followers have been using their administration affiliations imprudently to profit themselves.

Any of these reactions may be used in LPCVD, but the silane reaction is also done in APCVD.

Any subset of B is also well-ordered.

Any limit of regular ordinals is a limit of initial ordinals and thus is also initial but need not be regular.

Any new flag would also quickly become unlawful, due to wear and tear.

Although the 8080 was generally an 8-bit processor, it also had limited abilities to perform 16-bit operations: Any of the three 16-bit register pairs ( BC, DE, HL ) or SP could be loaded with an immediate 16-bit value ( using LXI ), incremented or decremented ( using INX and DCX ), or added to HL ( using DAD ).

* Combat knife: Any knife intended to be used by soldiers in the field, as a general-use tool, but also for fighting.

* plus VII: A-Ha's " Take on Me ", Gordon Lightfoot's " If You Could Read My Mind ", Amy Grant's " Good For Me ", Aretha Franklin's "( You Make Me Feel Like ) A Natural Woman " ( also Carole King ), Elvis Costello and the Attractions ' " Everyday I Write The Book ", and the Traveling Wilburys ' " Not Alone Any More ".

The Nijmegen Statement said: " Any form of Inquisition however subtle, not only harms the development of sound theology, it also causes irreparable damage to the credibility of the church ".

Any incidence of water is then used by migrating birds who also pass seeds with their droppings which will grow at the water's edge forming an oasis.

Any real mode operating system ( such as Xenix ) could also be made to run using OS / 2's virtual machine capabilities, subject to certain direct hardware access limitations.

Any decidable type system involves a trade-off: while it rejects many incorrect programs, it can also prohibit some correct, albeit unusual programs.

Any U. S. citizen with at least one year of residence on the island is also eligible for the official citizenship certificate.

Any potato variety can also be propagated vegetatively by planting tubers, pieces of tubers, cut to include at least one or two eyes, or also by cuttings, a practice used in greenhouses for the production of healthy seed tubers.

Any algebra whose elements are idempotent is also power-associative.

Any state joining the union later was also required to be a republic.

Any device that can store and playback multimedia may also be considered a media player such as in the case with the HD media player.

Any chemical species that is regenerated, such as a catalyst, also has a stoichiometric coefficient of zero.

Any domain name can also be a hostname, as long as the restrictions mentioned below are followed.

Any Englishman who married a Welsh woman also came under the Penal Laws of 1402.

Any container of food which has been heat-treated and then assumed to be airtight which shows signs of not being so, e. g., metal cans with pinprick holes from rust or mechanical damage, should also be discarded.