Equation 677 Database

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Magma 485196b9a65f…

magma 485196b9a65f
Size
705
Isomorphism class hash
485196b9a65fc82d7e97ac26b33f57d7ce3027f0e6a7d059531fe44028bada4f
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 21:20:04
Display reorder
704,145,74,171,186,146,72,187,172,144,73,188,173,148,77,170,189,149,75,168,190,147,76,191,169,151,80,177,184,78,152,185,178,79,150,183,179,83,154,176,180,81,155,181,174,153,82,182,175,164,162,163,167,165,166,159,160,157,158,156,161,675,673,674,672,535,344,561,518,536,342,516,562,534,343,517,563,538,347,560,521,539,345,558,519,537,346,520,559,533,339,552,524,340,531,522,553,341,532,523,554,338,529,555,527,336,530,525,556,528,337,526,557,545,543,544,541,542,540,551,549,546,547,548,550,664,666,665,667,49,198,570,47,50,199,45,571,48,200,46,572,52,201,573,43,53,202,574,44,51,203,42,575,55,196,568,38,197,56,36,569,195,54,37,567,192,58,564,41,193,59,39,565,57,194,40,566,648,649,650,651,652,653,654,655,658,656,657,659,685,686,684,687,299,321,274,279,297,322,280,275,298,323,281,273,295,320,270,278,296,318,271,276,294,319,277,272,290,312,265,285,313,288,286,266,314,289,287,264,315,293,268,284,316,291,282,269,292,317,283,267,300,301,302,303,304,305,306,307,311,309,310,308,701,703,700,702,398,91,625,647,396,92,645,626,397,90,646,624,401,94,628,643,399,95,629,644,400,93,642,627,404,89,631,638,87,402,636,632,88,403,637,630,85,407,634,641,86,405,639,635,406,84,640,633,414,415,416,417,418,419,412,413,410,408,409,411,691,688,690,689,231,68,254,224,232,66,222,252,233,67,223,253,230,71,257,227,228,69,255,225,229,70,226,256,237,63,260,219,64,238,220,258,65,239,221,259,62,236,263,218,60,234,216,261,235,61,217,262,250,251,249,246,247,248,241,242,243,244,245,240,662,661,663,660,434,10,461,429,432,11,430,459,433,9,431,460,437,6,457,428,435,7,458,426,436,8,427,456,440,0,467,420,2,438,421,465,1,439,422,466,4,443,463,423,5,441,424,464,442,3,425,462,452,450,451,455,453,454,447,448,445,446,444,449,694,693,695,692,598,207,620,579,599,208,580,618,597,209,581,619,594,206,623,578,595,204,621,576,596,205,577,622,589,213,615,585,214,590,586,616,215,588,587,617,212,592,614,584,210,593,582,612,591,211,583,613,601,602,600,604,605,603,607,608,609,610,611,606,682,683,681,680,505,20,482,501,506,18,502,480,504,19,503,481,508,23,485,500,509,21,483,498,507,22,499,484,511,15,488,492,16,512,493,486,17,510,494,487,14,514,491,495,12,515,496,489,513,13,497,490,479,477,478,475,476,474,470,468,472,473,471,469,696,698,699,697,350,329,376,392,348,327,390,377,349,328,391,375,353,325,372,395,351,326,373,393,352,324,394,374,356,335,382,387,333,354,388,383,334,355,389,381,331,359,378,386,332,357,384,379,358,330,385,380,368,366,367,371,369,370,363,364,361,362,360,365,671,668,670,669,124,28,100,115,125,29,116,101,123,27,114,99,120,24,96,118,121,25,97,119,122,26,117,98,130,34,106,113,35,131,111,107,33,129,112,105,30,126,102,109,31,127,110,103,128,32,108,104,143,141,142,139,140,138,134,132,136,137,135,133,676,678,677,679 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#e9460cea3e471d03fe1a4dfa5e68e64aa509c8601c2a885c863435b22f6faffe, 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 21:20:05 · history