Equation 677 Database

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Magma 844f59a0ec3d…

magma 844f59a0ec3d
Size
705
Isomorphism class hash
844f59a0ec3d349288e20e366d4c359213ba6dc644b96ae1ffcdfa329b7e6011
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 16:39:31
Display reorder
660,257,376,494,328,482,483,377,258,495,329,378,484,256,496,330,485,260,379,497,331,261,486,380,498,332,487,259,381,499,333,480,255,374,492,326,481,253,375,493,327,491,479,254,373,325,251,476,370,488,322,252,477,371,489,323,250,478,372,490,324,684,677,682,679,182,79,352,211,219,217,80,183,353,212,81,218,181,354,213,215,178,78,355,210,179,216,76,356,208,214,180,77,357,209,225,188,70,350,202,223,189,71,351,203,349,224,187,72,204,184,221,73,346,205,185,222,74,347,206,186,220,75,348,207,664,665,668,672,273,518,304,230,470,471,519,271,305,231,520,472,272,306,229,473,269,521,307,226,270,474,522,308,227,475,268,523,309,228,468,264,516,302,236,469,262,517,303,237,301,467,263,515,235,267,464,512,298,232,265,465,513,299,233,266,466,514,300,234,675,683,680,685,26,612,619,613,615,623,621,24,627,620,629,631,25,635,628,639,29,636,643,637,27,647,644,651,645,655,28,653,659,652,598,32,599,603,597,606,30,607,611,604,595,590,31,591,589,35,564,565,569,568,33,574,575,579,573,34,582,583,587,580,702,701,703,704,123,424,412,400,436,437,425,121,413,401,426,438,122,414,402,439,119,427,415,403,120,440,428,416,404,441,118,429,417,405,434,129,422,410,398,435,127,423,411,399,409,433,128,421,397,125,430,418,406,394,126,431,419,407,395,124,432,420,408,396,691,690,693,692,239,458,340,116,506,507,459,240,341,117,460,508,238,342,115,509,242,461,343,112,243,510,462,344,113,511,241,463,345,114,504,245,456,338,107,505,246,457,339,108,337,503,244,455,106,248,500,452,334,110,249,501,453,335,111,247,502,454,336,109,663,661,670,667,163,47,450,49,68,69,45,164,451,50,46,67,165,449,51,64,162,43,448,48,160,65,44,561,560,66,161,42,562,563,59,154,38,443,52,60,155,36,444,53,442,58,156,37,54,157,62,41,446,55,158,63,39,447,56,159,61,40,445,57,696,695,689,694,18,554,530,316,167,168,555,19,531,317,556,166,20,532,318,170,21,557,533,319,22,171,558,534,320,169,23,559,535,321,173,16,552,528,314,174,17,553,529,315,527,172,15,551,313,12,176,548,524,310,13,177,549,525,311,14,175,550,526,312,686,676,674,687,86,617,616,618,614,622,625,87,624,626,633,630,85,632,634,638,82,641,640,642,83,646,649,648,650,654,84,657,656,658,596,92,601,600,602,605,93,609,608,610,592,588,91,593,594,88,570,571,566,567,89,572,577,576,578,90,581,585,584,586,697,700,698,699,190,97,292,388,542,543,98,191,293,389,99,544,192,294,390,545,193,96,295,391,194,546,94,296,392,547,195,95,297,393,540,196,103,290,386,541,197,104,291,387,289,539,198,105,385,199,536,102,286,382,200,537,100,287,383,201,538,101,288,384,662,666,671,669,9,280,364,130,152,153,281,10,365,131,282,151,1,366,132,148,7,283,367,133,8,149,284,368,134,150,11,285,369,135,143,4,278,362,136,144,5,279,363,137,361,142,6,277,138,3,146,274,358,139,0,147,275,359,140,2,145,276,360,141,678,681,688,673 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#3866b47acdf4717a31e27879d6448be53ada0b89c1671a7aec66e55c44000764, 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 16:39:33 · history