Equation 677 Database

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Magma f23d98d48e1f…

magma f23d98d48e1f
Size
705
Isomorphism class hash
f23d98d48e1f8855164d327147c1bf4808416a9989f8c28ca51a1360efa07e6d
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 704) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-03 18:19:32
Display reorder
660,374,97,441,472,417,372,98,439,470,415,471,96,373,440,416,370,100,437,468,413,371,101,438,469,414,369,99,436,467,412,103,447,380,478,423,104,445,378,476,421,102,446,379,477,422,443,106,376,474,419,444,107,377,475,420,442,105,375,473,418,678,681,675,679,274,170,289,36,127,272,171,287,37,128,38,169,273,288,126,277,173,285,39,130,275,174,286,40,131,276,172,284,41,129,168,280,269,42,125,166,278,270,43,123,167,279,271,44,124,283,164,268,45,121,281,165,266,46,122,282,163,267,47,120,672,666,665,668,338,292,534,510,116,336,290,532,508,114,509,291,337,533,115,334,295,530,506,119,335,293,531,507,117,333,294,529,505,118,298,540,344,516,111,296,538,342,514,112,297,539,343,515,113,536,301,340,512,110,537,299,341,513,108,535,300,339,511,109,674,683,676,685,407,139,484,137,319,405,140,482,138,317,136,141,406,483,318,410,142,480,133,315,408,143,481,134,316,409,144,479,135,314,145,657,654,652,653,146,641,638,636,637,147,649,646,644,645,623,148,620,624,625,633,149,630,628,629,485,150,411,132,320,704,697,703,701,570,88,362,429,20,568,89,360,427,18,428,87,569,361,19,566,84,358,425,23,567,85,359,426,21,565,86,357,424,22,94,368,576,435,15,95,366,574,433,16,93,367,575,434,17,364,90,572,431,14,365,91,573,432,12,363,92,571,430,13,689,691,692,690,498,187,306,67,326,496,188,307,68,324,66,189,497,305,325,494,190,302,70,322,495,191,303,71,323,493,192,304,69,321,193,312,504,65,332,194,313,502,63,330,195,311,503,64,331,308,196,500,61,328,309,197,501,62,329,310,198,499,60,327,662,663,667,670,248,209,212,226,245,249,210,213,227,246,228,208,247,211,244,251,205,215,225,241,252,206,216,223,242,250,207,214,224,243,200,218,254,232,236,201,219,255,233,237,199,217,253,234,235,221,203,257,231,239,222,204,258,229,240,220,202,256,230,238,695,694,696,693,350,48,0,613,453,348,49,2,611,451,612,50,349,1,452,346,51,4,609,449,347,52,5,610,450,345,53,3,608,448,54,7,356,619,459,55,8,354,617,457,56,6,355,618,458,10,57,352,615,455,11,58,353,616,456,9,59,351,614,454,680,688,673,682,579,74,490,465,263,577,72,491,463,264,464,73,578,492,265,582,77,489,461,262,580,75,487,462,260,581,76,488,460,261,80,658,659,656,655,78,642,643,640,639,79,650,651,648,647,626,83,627,622,621,634,81,635,632,631,486,82,583,466,259,699,700,698,702,601,162,182,386,558,599,160,183,384,556,385,161,600,181,557,597,158,185,382,554,598,159,186,383,555,596,157,184,381,553,153,180,607,392,564,151,178,605,390,562,152,179,606,391,563,176,156,603,388,560,177,154,604,389,561,175,155,602,387,559,669,664,671,661,589,32,522,398,546,587,30,520,396,544,397,31,588,521,545,585,35,518,394,542,586,33,519,395,543,584,34,517,393,541,27,528,595,404,552,28,526,593,402,550,29,527,594,403,551,524,26,591,400,548,525,24,592,401,549,523,25,590,399,547,686,677,687,684 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 705 = 1 + 11*64, from a common submagma at infinity. C(E, M, k, B) adjoins a submagma M (m elements) of a model E to every group of a transversal design TD(k, g), g = |E| - m, so that every enlarged group is a copy of E and all of them share M; every block carries B, a model of order k in which x*x = x. Two elements of M multiply in M; an element of M or of group i with one of group i, in group i's copy of E; elements of different groups, in their block. It satisfies Equation 677 whenever E and B do. This magma is C(E, M, 11, B) with E = magma#7b2d22e166b1ff02dad840b7a1389a143f850a338adb3bda964b6fc81ff7fb8b, M = {60} in E, B = magma#abfd8e025ce71b705594dbbe1465dc1c7328d12d30e12d07906d7138f9d583bc. Labels: 0..m-1 are M, in increasing order of their labels in E; m + g*i + c (i < k, c < g) is point c of group i, which plays the c-th element of E outside M, in increasing order. A block's point in group i plays element i of B. TD(11, 64): MacNeish's product over GF(64); GF(64) = F_2[x]/(x^6 + x + 1); GF(p^r) = F_p[x]/(f) labels c_0 + c_1 x + ... as c_0 + c_1 p + ..., and point c of a group is the c-th element of the product in lexicographic order. Block (a, b), a and b in the product, meets group i in the point whose coordinate in each field is a + s_i b, s_i the element of that field labelled i, or b when the field has exactly i elements. Equation 255: satisfied. Idempotent elements: 45.

last edited by qawbecrdtey at 2026-10-03 18:19:33 · history