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, 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.

Conversely, a standard line on which voice service has been unsubscribed ( such as an ADSL dry loop ) may still accept calls to the 958 test exchange but not allow calls to standard numbers.

Conversely, Howard Marshall writes that the speeches were not entirely the inventions of the author and, while they may not be verbatim, nevertheless records the general idea.

Conversely, the withdrawal syndrome may also be a trigger for relapse.

Conversely, an annual grown under extremely favorable conditions may have highly successful seed propagation, giving it the appearance of being biennial or perennial.

Conversely, because space is expanding, and more distant objects are receding ever more quickly, light emitted by us today may never " catch up " to very distant objects.

Conversely it may generate too many points in areas where the curve is close to linear.

Conversely, methods of thinning the mucus may help to achieve pregnancy.

Conversely, sociology of law may help comparative law answer questions, such as: How do regulations in different legal systems really function in the respective societies?

Conversely, Henig acknowledges that if the US had been a member, its reluctance to engage in war with European states and to enact economic sanctions may have hampered the ability of the League to deal with international incidents.

Conversely, emigration may remove genetic material.

Conversely, a person may feel like he belongs to one state without having any legal relationship to it.

Conversely, Walter Burkert suggests that the Hellene cult worship of Poseidon as a horse god may be connected to the introduction of the horse and war-chariot from Anatolia to Greece around 1600 BC.

Conversely we have a b if and only if a < b or a ~ b. This is the reason for using the notation ""; "≤" can be confusing for a preorder that is not anti-symmetric, it may suggest that a ≤ b implies that a < b or a

Conversely, the government may put off improvements due to political sensitivity and special interests — even in cases of companies that are run well and better serve their customers ' needs.

Conversely Pringles may be termed " potato chips " in Britain, to distinguish them from traditional " crisps ".

Conversely, the quilter may choose to make the quilting disappear, using " invisible " nylon or polyester thread, thread that matches the quilt top, or stitching within the patchwork seams themselves ( commonly known as " stitch in the ditch ").

Conversely, an important faction may have an interest in helping fund the campaign of smaller factions with a very different political agenda, so that these smaller parties end up weakening their own agenda.

Conversely, most modern role-playing games encourage gamemasters to ignore their gaming systems if it makes for a more enjoyable story, even though they may not describe themselves as " storytelling " games.

Conversely, the rejection of syncretism, usually in the name of " piety " and " orthodoxy ", may help to generate, bolster or authenticate a sense of uncompromised cultural unity in a well-defined minority or majority.

Conversely, only the wiki users interested in a given project need look at its associated wiki pages, in contrast to high-traffic mailing lists which may burden subscribers with many messages, regardless of their relevance.

Conversely, members of a society may also shun or scapegoat members of the society who violate its norms.

Conversely, these fluids may metasomatically alter a rock, introducing new Rb and Sr into the rock ( generally during potassic alteration or calcic ( albitisation ) alteration.

Conversely, the loss of water and volatiles from a magma may cause it to essentially freeze or solidify.

Conversely, clothing may protect the environment from the clothing wearer, as with doctors wearing medical scrubs.

Conversely a large cargo, for example in structure relocation, may be disassembled for carriage on multiple vehicles and then reassembled in the correct order at the destination.