Equation 677 Database

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Magma 84fd9a00ae4b…

magma 84fd9a00ae4b
Size
705
Isomorphism class hash
84fd9a00ae4b2e483f1be5a2cf4f8f07cacf0270b50ec25e95f86174825f83e4
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 16:45:46
Display reorder
660,237,239,238,235,236,234,230,228,229,233,231,232,207,251,249,208,250,209,247,206,248,204,246,205,242,213,240,214,241,215,245,212,243,210,244,211,179,217,177,218,178,216,175,220,176,221,174,219,170,223,168,224,169,222,173,226,171,227,172,225,673,676,674,692,359,358,357,354,355,356,349,350,348,352,353,351,379,369,370,380,371,378,368,382,366,383,367,381,360,377,361,375,362,376,363,373,364,374,365,372,43,389,44,387,42,388,46,385,47,386,45,384,41,395,39,393,40,394,37,391,38,392,36,390,661,668,665,682,80,79,78,82,83,81,77,75,76,73,74,72,655,2,1,656,0,654,5,658,3,659,4,657,8,653,6,651,7,652,11,649,9,650,10,648,186,62,187,60,188,61,189,65,190,63,191,64,184,68,185,66,183,67,180,71,181,69,182,70,681,677,671,694,130,129,131,128,126,127,120,121,122,123,124,125,144,136,137,145,135,146,132,147,133,148,134,149,142,150,143,151,141,152,138,153,139,154,140,155,104,109,102,110,103,108,107,112,105,113,106,111,99,115,100,116,101,114,98,118,96,119,97,117,696,697,702,703,449,448,447,444,445,446,454,455,453,450,451,452,477,464,462,478,463,479,467,476,465,474,466,475,459,468,460,469,461,470,458,471,456,472,457,473,53,491,51,489,52,490,49,487,50,488,48,486,59,482,57,480,58,481,55,485,56,483,54,484,685,686,689,700,566,565,564,568,569,567,571,572,570,574,575,573,597,584,582,598,583,599,587,596,585,594,586,595,579,588,580,589,581,590,578,591,576,592,577,593,94,559,95,560,93,558,90,562,91,563,92,561,85,557,86,555,84,556,88,553,89,554,87,552,663,669,664,684,282,284,283,287,285,286,279,280,281,278,276,277,262,292,293,263,291,261,288,258,289,259,290,260,298,253,299,254,297,252,294,256,295,257,296,255,503,270,501,271,502,272,499,273,500,274,498,275,494,268,492,269,493,267,497,264,495,265,496,266,687,688,690,699,537,539,538,535,536,534,530,528,529,533,531,532,504,550,551,505,549,506,546,507,547,508,548,509,541,510,542,511,540,512,544,513,545,514,543,515,200,526,198,527,199,525,203,522,201,523,202,524,195,517,196,518,197,516,194,520,192,521,193,519,678,679,675,693,334,333,335,332,330,331,324,325,326,327,328,329,158,340,341,156,339,157,336,161,337,159,338,160,346,164,347,162,345,163,342,167,343,165,344,166,301,317,302,315,300,316,304,313,305,314,303,312,307,323,308,321,306,322,310,319,311,320,309,318,695,698,701,704,403,402,404,405,406,407,400,401,399,396,397,398,425,409,410,423,408,424,412,421,413,422,411,420,415,431,416,429,414,430,418,427,419,428,417,426,13,433,14,434,12,432,16,436,17,437,15,435,19,439,20,440,18,438,22,442,23,443,21,441,662,666,667,683,630,632,631,635,633,634,627,628,629,626,624,625,610,641,639,611,640,609,637,606,638,607,636,608,647,601,645,602,646,600,643,604,644,605,642,603,27,618,28,619,29,620,26,621,24,622,25,623,33,616,34,617,35,615,32,612,30,613,31,614,670,680,672,691 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#3e7f78778326128ca89bcdb69266df7c07c66aee73c2a2e36b24ead92b52079d, 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 16:45:47 · history