Equation 677 Database

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Magma 6d71e2914e19…

magma 6d71e2914e19
Size
705
Isomorphism class hash
6d71e2914e195277d2efbf0993e93381a48faad9a18b963a26afbcda6d799747
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 21:10:13
Display reorder
660,364,142,102,555,439,362,140,103,556,440,363,141,104,557,441,367,145,554,438,105,365,106,143,552,436,144,107,366,553,437,148,100,561,359,445,146,101,562,360,446,147,99,563,361,447,151,96,560,358,444,97,149,558,356,442,357,98,150,559,443,679,680,675,682,463,81,276,499,265,464,79,277,500,263,465,80,275,501,264,462,77,498,261,272,460,273,78,496,262,76,274,461,497,260,87,282,505,469,271,85,283,506,470,269,86,281,507,471,270,83,278,504,468,267,279,84,502,466,268,467,280,82,503,266,662,664,668,665,301,35,511,292,475,299,36,512,290,476,300,34,513,291,477,297,38,295,474,510,298,508,39,293,472,37,509,296,294,473,33,517,287,307,481,31,518,288,305,482,32,519,289,306,483,29,516,286,303,480,514,30,284,304,478,302,515,28,285,479,681,673,678,677,406,180,567,522,4,404,181,568,520,2,405,179,569,521,3,409,176,525,7,566,407,564,177,523,5,178,565,408,524,6,186,641,639,638,636,187,649,647,646,645,185,657,655,654,653,182,630,628,633,632,570,183,526,410,0,411,571,184,527,1,700,697,703,704,376,119,395,487,385,374,117,396,488,383,375,118,397,489,384,379,115,486,381,394,377,392,116,484,382,114,393,378,485,380,110,401,493,371,391,108,402,494,372,389,109,403,495,373,390,113,400,492,370,387,398,111,490,368,388,369,399,112,491,386,690,689,694,692,208,15,232,240,427,206,16,230,241,428,207,14,231,239,429,211,18,236,426,235,209,233,19,237,424,17,234,210,238,425,13,227,246,203,433,11,228,247,204,434,12,229,245,205,435,9,226,242,202,432,224,10,243,200,430,201,225,8,244,431,661,669,663,672,611,163,610,130,57,613,161,612,131,55,614,162,615,129,56,608,159,126,53,609,605,604,160,127,54,158,607,606,128,52,154,622,121,623,63,152,625,122,624,61,153,627,120,626,62,157,621,124,620,59,616,155,125,617,60,618,619,156,123,58,695,696,691,693,586,173,587,451,415,588,174,589,452,416,591,175,590,453,417,585,172,450,414,584,580,581,170,448,412,171,582,583,449,413,164,599,457,598,421,165,600,458,601,422,166,602,459,603,423,167,596,456,597,420,593,168,454,592,418,595,594,169,455,419,686,685,674,676,139,66,574,25,94,137,64,572,23,95,138,65,573,24,93,135,69,21,90,577,136,575,67,22,91,68,576,134,20,92,72,643,637,642,640,70,650,644,651,648,71,658,652,659,656,75,635,634,631,629,578,73,27,133,89,132,579,74,26,88,702,701,699,698,543,215,193,531,250,544,216,191,532,248,545,217,192,533,249,542,214,530,253,189,540,190,212,528,251,213,188,541,529,252,221,199,537,549,256,222,197,538,550,254,223,198,539,551,255,220,195,536,548,259,196,218,534,546,257,547,194,219,535,258,666,670,671,667,313,41,333,353,324,311,42,334,354,325,312,40,332,355,323,309,44,352,320,336,310,337,45,350,321,43,335,308,351,322,47,339,344,319,330,48,340,345,317,331,46,338,346,318,329,50,342,347,315,326,343,51,348,316,327,314,341,49,349,328,687,688,683,684 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#dc2fe3473be348561d898626a2f45bbebd7964bafd5487f2fff34f8adc67b3cf, 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 21:10:14 · history