Equation 677 Database

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Magma 2d3978231ae5…

magma 2d3978231ae5
Size
705
Isomorphism class hash
2d3978231ae5653e8c53382505b2d89f085bea0917b6e35df96b16acd97bd187
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 21:12:39
Display reorder
660,265,388,495,126,435,263,493,127,433,386,264,387,494,128,434,268,498,391,129,438,266,496,389,130,436,267,497,390,131,437,501,271,394,132,441,133,499,269,392,439,500,270,393,134,440,274,504,397,135,444,272,502,395,136,442,273,503,396,137,443,673,678,676,680,362,70,529,298,202,363,527,296,200,71,364,69,528,297,201,365,532,66,294,198,366,530,67,295,199,367,531,68,293,197,535,368,76,289,208,287,533,369,77,206,534,370,75,288,207,371,538,72,292,204,372,536,73,290,205,373,537,74,291,203,672,665,669,667,211,308,447,376,576,209,445,374,574,309,210,310,446,375,575,214,450,307,379,579,212,448,305,377,577,213,449,306,378,578,453,217,299,382,582,380,451,215,300,580,452,216,301,381,581,220,456,302,385,585,218,454,303,383,583,219,455,304,384,584,674,684,675,679,43,336,15,507,327,44,16,505,328,334,42,335,17,506,329,46,14,339,510,326,47,12,337,508,324,45,13,338,509,325,348,49,342,513,333,511,349,50,340,331,347,48,341,512,332,52,653,652,657,656,53,345,343,514,330,51,346,344,515,323,700,698,704,703,36,146,159,471,78,37,160,469,79,144,38,145,161,470,80,39,158,149,474,81,40,156,147,472,82,41,157,148,473,83,150,34,141,477,84,475,151,35,142,85,152,33,143,476,86,30,153,140,480,87,31,154,138,478,88,32,155,139,479,89,692,689,694,693,312,222,7,483,564,313,8,481,562,223,311,221,6,482,563,315,10,225,486,567,316,11,226,484,565,314,9,224,485,566,5,318,228,489,570,487,3,319,229,568,4,317,227,488,569,321,0,231,492,573,322,2,232,490,571,320,1,230,491,572,664,668,661,666,21,103,459,247,249,22,457,245,250,104,23,102,458,246,248,20,462,106,638,639,18,460,107,635,634,19,461,105,637,636,465,27,109,644,645,641,463,28,110,640,464,29,108,643,642,26,468,112,651,650,24,466,113,647,646,25,467,111,649,648,696,695,690,691,118,588,624,167,259,119,622,165,257,586,117,587,623,166,258,114,627,591,163,262,115,625,589,164,260,116,626,590,162,261,630,124,594,173,254,171,628,125,592,255,629,123,593,172,256,120,633,597,169,253,121,631,595,170,251,122,632,596,168,252,681,683,685,687,190,179,518,400,553,188,516,398,551,177,189,178,517,399,552,186,521,175,403,556,187,519,176,401,554,185,520,174,402,555,524,196,183,406,559,404,522,194,181,557,523,195,182,405,558,192,659,658,654,655,193,525,184,407,560,191,526,180,408,561,699,702,697,701,358,279,612,58,423,356,610,59,421,280,357,278,611,57,422,361,615,275,54,426,359,613,276,55,424,360,614,277,56,425,618,353,285,64,429,65,616,354,286,427,617,355,284,63,428,352,621,281,60,432,350,619,282,61,430,351,620,283,62,431,670,662,663,671,90,243,411,541,600,91,409,539,598,244,92,242,410,540,599,93,414,239,544,603,94,412,240,542,601,95,413,241,543,602,417,96,234,547,606,545,415,97,235,604,416,98,233,546,605,99,420,237,550,609,100,418,238,548,607,101,419,236,549,608,682,686,688,677 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#dd5d8cb242321da00ce62fc2d476849be658b6b0a3d2fd229095425016dc303c, 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 21:12:40 · history