Equation 677 Database

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Magma 9ab628ebc7f8…

magma 9ab628ebc7f8
Size
705
Isomorphism class hash
9ab628ebc7f84b642eeb9f2516ced8cf5cf0703c33df2d066bf8b302c72a10ee
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 18:21:23
Display reorder
660,118,36,563,351,511,119,37,564,352,512,117,35,565,353,513,32,114,562,350,510,115,33,560,348,508,34,116,561,349,509,569,109,42,357,517,570,110,43,358,518,571,108,41,359,519,112,568,38,356,516,113,566,39,354,514,111,567,40,355,515,673,680,683,684,63,232,363,183,179,61,233,364,184,177,62,231,365,185,178,228,59,362,182,175,60,229,360,180,176,230,58,361,181,174,369,54,238,189,170,370,52,239,190,168,371,53,237,191,169,57,368,234,188,173,55,366,235,186,171,56,367,236,187,172,666,670,662,661,200,75,24,263,248,198,73,25,261,246,199,74,23,262,247,71,203,20,259,251,201,72,21,260,249,70,202,22,258,250,30,195,66,254,243,31,196,64,252,244,29,197,65,253,245,194,26,69,257,242,192,27,67,255,240,193,28,68,256,241,675,677,685,674,2,284,523,90,47,3,282,524,88,48,4,283,525,89,46,287,5,522,93,50,6,285,520,91,51,286,7,521,92,49,641,639,279,637,636,649,647,280,644,645,657,655,281,652,653,629,630,278,633,632,1,526,276,94,45,0,527,277,95,44,703,698,700,704,575,127,303,399,17,576,128,304,400,18,577,126,305,401,19,130,574,302,398,16,572,131,300,396,14,129,573,301,397,15,309,581,125,405,8,310,582,123,406,9,311,583,124,407,10,580,308,121,404,11,578,306,122,402,12,579,307,120,403,13,690,689,692,694,375,81,269,419,487,376,79,267,420,488,377,80,268,421,489,77,374,265,418,486,372,78,266,416,484,76,373,264,417,485,275,381,87,425,493,273,382,85,426,494,274,383,86,427,495,380,271,83,424,492,378,272,84,422,490,379,270,82,423,491,664,667,672,663,325,225,162,455,134,326,226,163,456,132,324,227,164,457,133,224,328,165,454,137,329,222,166,452,135,223,327,167,453,136,160,331,216,461,140,161,332,217,462,138,159,330,218,463,139,334,156,219,460,143,335,157,220,458,141,333,158,221,459,142,691,695,696,693,347,99,475,387,619,345,100,476,388,620,346,101,477,389,621,98,343,474,386,618,344,96,472,384,616,97,342,473,385,617,481,338,105,393,625,482,336,106,394,626,483,337,107,395,627,341,480,104,392,624,339,478,102,390,622,340,479,103,391,623,676,688,679,682,468,209,611,531,410,469,207,612,532,408,470,208,613,533,409,205,467,610,530,413,465,206,608,528,411,204,466,609,529,412,643,640,215,642,638,651,648,213,650,646,659,656,214,658,654,634,635,211,631,628,471,614,212,534,414,464,615,210,535,415,701,697,702,699,499,296,431,551,587,500,294,432,552,588,501,295,433,553,589,299,498,430,550,586,496,297,428,548,584,298,497,429,549,585,437,505,291,557,593,438,506,292,558,594,439,507,293,559,595,504,436,290,556,592,502,434,288,554,590,503,435,289,555,591,669,671,665,668,153,314,443,599,539,154,312,444,600,540,155,313,445,601,541,317,152,442,598,538,150,315,440,596,536,316,151,441,597,537,449,144,320,605,545,450,145,318,606,546,451,146,319,607,547,147,448,323,604,544,148,446,321,602,542,149,447,322,603,543,686,681,678,687 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#7bddf6e5b82b5432712e2579d3d5db84306ca98ed650c79ff87e357573a5998e, 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 18:21:24 · history