Equation 677 Database

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Magma 2bbeb412c082…

magma 2bbeb412c082
Size
705
Isomorphism class hash
2bbeb412c082a22ba0fafcdeeb0bef1ec45dd71671ee05e8e46515aec8b44d3b
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 17:29:52
Display reorder
660,242,482,400,494,304,243,483,495,305,401,241,484,402,496,306,485,238,403,497,307,486,239,404,498,308,487,240,405,499,309,248,480,398,492,302,249,481,399,493,303,247,479,397,491,301,244,476,394,488,298,245,477,395,489,299,246,478,396,490,300,684,673,682,679,29,178,203,376,36,30,179,377,34,204,28,180,202,378,35,181,32,206,379,39,182,33,207,380,37,183,31,205,381,38,27,184,209,374,42,25,185,210,375,40,26,186,208,373,41,23,187,212,370,45,24,188,213,371,43,22,189,211,372,44,664,665,668,672,221,470,518,316,251,222,471,317,252,519,220,472,520,318,250,473,224,521,319,254,474,225,522,320,255,475,223,523,321,253,219,468,516,314,257,217,469,517,315,258,218,467,515,313,256,215,464,512,310,260,216,465,513,311,261,214,466,514,312,259,675,683,680,685,59,614,613,619,615,60,622,627,623,620,58,630,628,635,631,638,62,637,643,639,646,63,645,651,647,654,61,652,659,655,65,598,597,603,599,66,606,604,611,607,64,590,589,595,591,68,566,565,569,568,69,574,572,579,575,67,582,580,587,583,702,701,703,704,82,436,95,292,424,83,437,293,425,96,84,438,94,294,426,439,85,98,295,427,440,86,99,296,428,441,87,97,297,429,88,434,101,290,422,89,435,102,291,423,90,433,100,289,421,91,430,104,286,418,92,431,105,287,419,93,432,103,288,420,690,692,693,689,75,506,458,141,268,73,507,139,269,459,74,508,460,140,270,509,71,461,137,271,510,72,462,138,272,511,70,463,136,273,81,504,456,132,266,79,505,457,130,267,80,503,455,131,265,77,500,452,135,262,78,501,453,133,263,76,502,454,134,264,661,662,670,667,157,364,21,450,0,158,365,451,2,19,159,366,20,449,3,367,156,17,448,1,368,154,18,561,560,369,155,16,562,563,163,362,12,443,7,164,363,10,444,8,165,361,11,442,9,162,358,15,446,6,160,359,13,447,4,161,360,14,445,5,696,695,691,694,237,328,554,530,53,235,329,531,54,555,236,330,556,532,52,331,233,557,533,56,332,234,558,534,57,333,232,559,535,55,228,326,552,528,51,226,327,553,529,49,227,325,551,527,50,231,322,548,524,47,229,323,549,525,48,230,324,550,526,46,686,674,676,687,171,616,617,612,618,169,624,621,626,625,170,632,633,629,634,640,167,641,636,642,648,168,649,644,650,656,166,657,653,658,177,600,601,596,602,175,608,609,605,610,176,592,593,588,594,173,570,571,564,567,174,576,577,573,578,172,584,585,581,586,698,700,697,699,200,542,285,340,412,201,543,341,413,283,199,544,284,342,414,545,196,281,343,415,546,197,282,344,416,547,198,280,345,417,191,540,276,338,410,192,541,274,339,411,190,539,275,337,409,194,536,279,334,406,195,537,277,335,407,193,538,278,336,408,663,666,671,669,143,117,352,388,127,144,115,389,128,353,142,116,354,390,129,113,146,355,391,126,114,147,356,392,124,112,145,357,393,125,149,108,350,386,118,150,106,351,387,119,148,107,349,385,120,152,111,346,382,121,153,109,347,383,122,151,110,348,384,123,678,681,688,677 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#58222ccd0574e7adf03b9b32a848bfc3e464df8d7127a3e76f96a819fe65341a, 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 17:29:53 · history