Equation 677 Database

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Magma 57865cd3e856…

magma 57865cd3e856
Size
705
Isomorphism class hash
57865cd3e856f66395da628fb9a955cacffd208bdb66360a40f3f525e658ebaf
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 18:22:23
Display reorder
660,142,239,420,509,543,143,240,418,507,541,508,238,144,419,542,242,145,416,505,539,243,146,417,506,540,241,147,415,504,538,148,245,411,500,534,149,246,409,498,532,150,244,410,499,533,248,151,414,503,537,249,152,412,501,535,247,153,413,502,536,680,684,674,676,19,315,326,348,303,20,313,327,346,301,347,314,18,325,302,318,22,329,344,306,316,23,330,345,304,317,21,328,343,305,17,321,332,339,309,15,319,333,337,307,16,320,331,338,308,324,13,335,342,312,322,14,336,340,310,323,12,334,341,311,662,663,667,669,257,31,579,531,172,258,32,577,529,173,530,30,256,578,174,34,260,575,527,175,35,261,576,528,176,33,259,574,526,177,255,29,570,522,170,253,27,568,520,171,254,28,569,521,169,25,251,573,525,166,26,252,571,523,167,24,250,572,524,168,682,687,677,686,158,656,654,655,658,159,640,638,639,642,647,648,157,646,650,624,154,622,623,626,632,155,630,631,634,616,156,614,615,618,164,284,276,281,512,165,285,277,279,510,163,286,278,280,511,607,160,606,608,609,287,161,274,282,513,288,162,275,283,514,704,700,703,699,221,372,396,52,444,222,370,394,53,442,54,371,220,395,443,368,224,392,55,440,369,225,393,56,441,367,223,391,57,439,219,363,387,50,435,217,361,385,51,433,218,362,386,49,434,366,215,390,46,438,364,216,388,47,436,365,214,389,48,437,694,693,690,692,178,485,461,591,267,179,483,459,589,265,590,484,180,460,266,481,181,457,587,263,482,182,458,588,264,480,183,456,586,262,184,476,452,582,273,185,474,450,580,271,186,475,451,581,272,479,187,455,585,269,477,188,453,583,270,478,189,454,584,268,672,661,666,665,200,73,384,103,107,201,74,382,104,108,105,75,199,383,106,72,196,380,102,110,70,197,381,100,111,71,198,379,101,109,191,79,375,94,113,192,80,373,95,114,190,81,374,96,112,78,194,378,97,116,76,195,376,98,117,77,193,377,99,115,695,689,696,691,118,473,497,134,603,119,471,495,135,601,133,472,120,496,602,469,121,493,130,599,470,122,494,131,600,468,123,492,132,598,124,464,488,140,594,125,462,486,141,592,126,463,487,139,593,467,127,491,136,597,465,128,489,137,595,466,129,490,138,596,681,688,678,679,4,657,659,652,653,5,641,643,636,637,644,649,3,651,645,625,1,627,620,621,633,0,635,629,628,617,2,619,612,613,10,449,517,44,38,11,447,515,45,36,9,448,516,43,37,610,6,611,605,604,446,7,518,41,39,445,8,519,42,40,702,698,697,701,293,567,432,208,66,294,565,430,209,64,210,566,292,431,65,563,289,428,211,69,564,290,429,212,67,562,291,427,213,68,299,558,423,206,61,300,556,421,207,62,298,557,422,205,63,561,295,426,202,60,559,296,424,203,58,560,297,425,204,59,670,668,671,664,91,555,226,408,360,92,553,227,406,358,407,554,93,228,359,551,90,229,404,356,552,88,230,405,357,550,89,231,403,355,82,546,232,399,351,83,544,233,397,349,84,545,234,398,350,549,85,235,402,354,547,86,236,400,352,548,87,237,401,353,675,673,685,683 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#7d1a9ea30af90bcd4d08abf0386c83ad32096e29a3d77362c99ba04d722859db, 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 18:22:24 · history