Conversely, if ( A, m, e, inv ) is a group object in one of those categories, then m necessarily coincides with the given operation on A, e is the inclusion of the given identity element on A, inv is the inversion operation and A with the given operation is an abelian group.

Conversely, discretionary behavior is motivated by internal values and is seen as more cooperative and therefore ideal within a group.

Conversely, other British acts such as Wang Chung, Breathe and Murray Head, as well as the Anglo-Australian duo Air Supply, are one-hit wonders in the UK but not in the US, and the American group 3T, best known in their homeland as being the three sons of Tito Jackson of The Jackson 5, along with other bands such as Blind Melon and Deep Blue Something, are one-hit wonders in the US but not in the UK.

Conversely, a group may also devolve to an earlier stage if unable to resolve outstanding issues in a particular stage.

Conversely, it is a consequence of the subsequent conclusions of the theorem that any compact Lie group is isomorphic to a matrix group.

Conversely, any affine linear transformation extends uniquely to a projective linear transformations, so the affine group is a subgroup of the projective group.

Conversely, if n is prime, then there exists a primitive root modulo n, or generator of the group ( Z / nZ )*.

* Conversely, a letter or group of letters can correspond to different phonemes in different contexts ( as th does in English ; originally this stood for a single phoneme, which then split ).

Given then a normal extension L of K, with automorphism group Aut ( L / K ) = G, and containing α, any element g ( α ) for g in G will be a conjugate of α, since the automorphism g sends roots of p to roots of p. Conversely any conjugate β of α is of this form: in other words, G acts transitively on the conjugates.

Conversely, given a Hopf algebra whose coalgebra structure is given above, we can recover a formal group law F from it.

Conversely, given a left kG module M, then M is a k vector space, and multiplication with an element g of G yields a k-linear automorphism of M ( since g is invertible in kG ), which describes a group homomorphism G → GL ( M ).

Conversely, Austereo's Triple M group of stations have suffered heavily from increased competition from new station Vega 95. 3 and Vega 91. 5 in Sydney and Melbourne respectively, with the stations in Melbourne and Sydney recording some of their lowest ratings of all time.

Conversely, if one pottery-type suddenly replaces a great diversity of pottery types in an entire region this might be interpreted as a new group migrating in with this new style.

Conversely, if the holonomy group of the Riemannian manifold M is contained in Sp ( k ), choose complex structures I < sub > x </ sub >, J < sub > x </ sub > and K < sub > x </ sub > on T < sub > x </ sub > M which make T < sub > x </ sub > M into a quaternionic vector space.

Conversely, symmetric tensors are defined as invariants: given the natural action of the symmetric group on the tensor algebra, the symmetric tensors are the subspace on which the symmetric group acts trivially.

Conversely, if G contains a proper non-trivial normal subgroup N, then the composition of the natural surjective group homomorphism G → G / N with the regular representation of G / N produces a representation π of G which has kernel N. Taking χ to be the character of some non-trivial subrepresentation of π, we have a character satisfying the hypothesis in the direct statement above.

Conversely if a Kleinian group has no nontrivial torsion elements then it is the fundamental group of a hyperbolic 3-manifold.

Conversely, the conservative group Americans for Constitutional Action stated Mathias agreed with their positions only 16 % of the time.

To summarize, M is a symmetric space G / K with a compact isotropy group K. Conversely, symmetric spaces with compact isotropy group are Riemannian symmetric spaces, although not necessarily in a unique way.

If neither A nor B includes the idea of existence, then " some A are B " simply adjoins A to B. Conversely, if A or B do include the idea of existence in the way that " triangle " contains the idea " three angles equal to two right angles ", then " A exists " is automatically true, and we have an ontological proof of A's existence.

Conversely, Scheme contains multiple coherent subsets that suffice to construct the rest of the language as library macros, and so the language designers do not even bother to say which portions of the language must be implemented as language constructs, and which must be implemented as parts of a library.

Conversely SVG is an ideal PDL for print-oriented uses, as it contains all the functionality required to place each glyph and image in a chosen location on the final page.

Each convex set containing X must ( by the assumption that it is convex ) contain all convex combinations of points in X, so the set of all convex combinations is contained in the intersection of all convex sets containing X. Conversely, the set of all convex combinations is itself a convex set containing X, so it also contains the intersection of all convex sets containing X, and therefore the sets given by these two definitions must be equal.

Conversely, experiments with robotic dummies were indeed able to induce some recruitment, which should not have been possible if the dance contains no information.

Conversely, an energy level is said to be degenerate if it contains two or more different states.

Conversely, the vowel marks of the Tigrinya abugida and the Amharic abugida ( ironically, the original source of the term " abugida ") have been so completely assimilated into their consonants that the modifications are no longer systematic and have to be learned as a syllabary rather than as a segmental script.

Conversely, an adiabatic process that is irreversible and extracts no work is in an isenthalpic process, such as viscous drag, progressing towards a nonnegative change in entropy.

Conversely, British English favours fitted as the past tense of fit generally, whereas the preference of American English is more complex: AmEng prefers fitted for the metaphorical sense of having made an object " fit " ( i. e., suited ) for a purpose ; in spatial transitive contexts, AmEng uses fitted for the sense of having made an object conform to an unchanged object that it surrounds ( e. g., " fitted X around Y ") but fit for the sense of having made an object conform to an unchanged object that surrounds it ( e. g., " fit X into Y "); and for the spatial senses ( both intransitive and transitive ) of having been matching with respect to contour, with no alteration of either object implied, AmEng prefers fit (" The clothes fit.

Conversely, if no advantage is gained from kicking the ball, play should continue.

Conversely, a very severe bit, in the right hands, can transmit subtle commands that cause no pain to the horse.

That is, the motivational internalist believes that there is an internal, necessary connection between one's conviction that X ought to be done and one's motivation to do X. Conversely, the motivational externalist ( or moral externalist ) claims that there is no necessary, internal connection between moral convictions and moral motives.

Conversely, John Calvin, Albert Barnes Adam Clarke, John Gill, and John Wesley amongst many other have affirmed this as divine truth and found no problem with its historicity.

Conversely, Baptists are underrepresented, a reflection of their quite recent expansion in numbers ; there has been only one Roman Catholic president, although they are currently the largest single denomination, and there have been no Lutheran, Pentecostal, or Latter Day Saint presidents.

Conversely, once the hardware and software for an anti-lock braking system has been designed to meet its required deadlines, no further performance gains are obligatory.

Conversely, no individual is shielded from the consequences of poor judgement or bad timing.

Conversely, Elijah Delmedigo ( c. 1458 – c. 1493 ), in his Bechinat ha-Dat endeavored to show that the Zohar could not be attributed to Shimon bar Yochai, arguing that if it were his work, the Zohar would have been mentioned by the Talmud, as has been the case with other works of the Talmudic period, that had bar Yochai known by divine revelation the hidden meaning of the precepts, his decisions on Jewish law from the Talmudic period would have been adopted by the Talmud, that it would not contain the names of rabbis who lived at a later period than that of Simeon ; and that if the Kabbalah was a revealed doctrine, there would have been no divergence of opinion among the Kabbalists concerning the mystic interpretation of the precepts.

Conversely, white men / non-white women couples show either very little or no differences in divorce rates.

Conversely, some species have little or no circulatory system at all, transporting oxygen in the coelomic fluid that fills their body cavity.

Conversely, the influence of the data at any given point on the initial line propagates with the finite velocity c: there is no effect outside a triangle through that point whose sides are characteristic curves.

Conversely, lutefisk prepared from pollock or haddock emits almost no odor.

Conversely, we understand Cleopatra at her death as the transcendent queen of “ immortal longings ” because the container of her mortality can no longer restrain her: unlike Antony, she never melts, but sublimates from her very earthly flesh to ethereal fire and air .”

Conversely we come to understand Cleopatra in that the container of her mortality can no longer restrain her.

Conversely, they have no recognizable homologs in archea and bacteria and are thus part of the " eukaryotic signature genes.

Conversely, opponents of changing saw no need to change, with businesses and the fire department fearing the expense of changing and the consequences of forgetting the community's history as West Paterson.

Conversely, in the category of rings, there are no kernels in the category-theoretic sense ; indeed, this category does not even have zero morphisms.

Conversely, the selling price of a product made in a participating country and sold in a country that does not participate, bears no part of the tax burden of the country in which it is sold ( as do the domestic products it is competing with ).

Conversely, the HMV store chain exists in Japan ( though no longer owned by HMV Group ), but it cannot use the His Master's Voice motto or logo ; its logo is a stylized image of a gramophone only.

Conversely in the UK, " It is important to understand that there is no right to strike in UK law .".

Conversely there have been a small number of aircraft designs which have no separate wing, but use the fuselage to generate lift.

Conversely, jurisdictions that generally allow this might forbid it at a particular intersection with a " no turn on red " sign, or put a green arrow to indicate specifically when a turn is allowed without having to yield to pedestrians ( this is usually when traffic from the perpendicular street is making a turn onto one's street and thus no pedestrians are allowed in the intersection anyway ).