Equation 677 Database

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Magma 2d2bedccfb3b…

magma 2d2bedccfb3b
Size
705
Isomorphism class hash
2d2bedccfb3b53aef5ba365a6c7a4626d38d35e607d01f8b4398512f322a3f65
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 17:21:40
Display reorder
660,493,407,346,420,216,217,408,494,347,421,218,406,492,345,419,496,219,410,349,423,497,220,411,350,424,221,495,409,348,422,344,222,491,405,418,223,489,403,342,416,224,490,404,343,417,487,225,401,340,414,488,226,402,341,415,486,227,400,339,413,680,673,679,683,318,284,308,469,61,62,282,319,306,470,60,283,320,307,468,317,64,280,304,472,315,65,281,305,473,63,316,279,303,471,314,67,324,290,467,68,325,288,312,465,66,326,289,313,466,323,70,286,310,463,321,71,287,311,464,322,69,285,309,462,666,672,661,670,555,518,358,40,96,97,519,556,359,41,98,517,554,357,39,558,99,521,361,36,559,100,522,362,37,101,557,520,360,38,356,102,553,516,46,103,551,514,354,47,104,552,515,355,45,549,105,512,352,42,550,106,513,353,43,548,107,511,351,44,674,675,685,687,623,620,627,621,186,187,629,631,635,628,188,612,615,619,613,647,189,644,651,645,655,190,652,659,653,191,639,636,643,637,611,184,607,605,606,185,591,589,595,590,183,599,597,603,598,574,180,572,577,576,583,181,581,587,580,375,182,278,535,277,704,702,703,697,251,457,236,209,109,110,458,249,234,207,108,456,250,235,208,247,112,460,239,205,248,113,461,237,206,111,246,459,238,204,231,115,242,455,215,116,240,453,232,213,114,241,454,233,214,245,118,451,230,211,243,119,452,228,212,244,117,450,229,210,689,690,693,692,395,506,481,543,173,171,507,396,482,544,172,505,394,480,542,398,169,509,484,546,399,170,510,485,547,168,397,508,483,545,479,179,393,504,541,177,391,502,477,539,178,392,503,478,540,389,175,500,475,537,390,176,501,476,538,388,174,499,474,536,671,667,669,663,261,267,433,89,142,143,268,262,434,87,141,269,263,432,88,260,138,266,436,85,258,139,264,437,86,140,259,265,435,84,431,133,252,273,95,134,253,274,429,93,132,254,275,430,94,255,136,272,427,91,256,137,270,428,92,257,135,271,426,90,695,691,696,694,370,30,567,530,166,167,31,371,568,531,165,32,369,566,529,373,162,33,570,533,374,163,34,571,534,164,372,35,569,532,565,157,368,28,528,158,366,29,563,526,156,367,27,564,527,364,160,24,561,524,365,161,25,562,525,363,159,26,560,523,686,688,678,676,626,625,622,624,155,153,633,634,630,632,154,617,618,614,616,650,151,649,646,648,658,152,657,654,656,150,642,641,638,640,604,146,610,609,608,144,594,593,588,592,145,602,601,596,600,579,149,578,573,575,586,147,585,582,584,498,148,425,276,412,699,698,700,701,294,51,334,200,2,1,52,295,335,198,0,53,296,333,199,293,5,50,337,203,291,3,48,338,201,4,292,49,336,202,332,8,300,57,195,6,301,58,330,196,7,302,59,331,197,299,11,56,328,194,297,9,54,329,192,298,10,55,327,193,668,662,664,665,383,16,77,445,130,131,17,384,75,446,129,15,382,76,444,386,126,12,73,448,387,127,13,74,449,128,385,14,72,447,83,121,381,22,443,122,379,23,81,441,120,380,21,82,442,377,124,18,79,439,378,125,19,80,440,376,123,20,78,438,681,684,682,677 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#4f5c530836fd0cc12915654d9cb933b30b1ebf0f1cb96882ec953efd42c5ac65, 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 17:21:42 · history