Equation 677 Database

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Magma 8ef549eff6c0…

magma 8ef549eff6c0
Size
705
Isomorphism class hash
8ef549eff6c0ec2dd3bca8c425e5ad95ecf754bf856280a06eb1bc7c1f9e987c
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 15:34:17
Display reorder
660,476,475,474,478,479,477,473,471,472,469,470,468,440,438,439,443,441,442,435,436,437,434,432,433,452,450,451,455,453,454,447,448,449,446,444,445,464,462,463,467,465,466,459,460,461,458,456,457,186,187,188,189,190,191,184,185,183,180,181,182,677,684,682,683,274,273,275,272,270,271,264,265,266,267,268,269,229,230,228,232,233,231,235,236,234,238,239,237,240,241,242,243,244,245,246,247,248,249,250,251,254,252,253,257,255,256,260,258,259,263,261,262,292,293,291,288,289,290,298,299,297,294,295,296,661,669,667,668,34,33,35,32,30,31,24,25,26,27,28,29,487,488,486,490,491,489,485,483,484,481,482,480,500,498,499,503,501,502,495,496,497,494,492,493,510,511,512,513,514,515,508,509,507,504,505,506,88,89,87,84,85,86,94,95,93,90,91,92,676,687,675,688,656,655,654,658,659,657,653,651,652,649,650,648,620,618,619,623,621,622,615,616,617,614,612,613,632,630,631,635,633,634,627,628,629,626,624,625,644,642,643,647,645,646,639,640,641,638,636,637,46,47,45,42,43,44,37,38,36,40,41,39,698,700,701,704,359,358,357,354,355,356,349,350,348,352,353,351,371,369,370,367,368,366,362,360,361,365,363,364,381,382,383,380,378,379,372,373,374,375,376,377,343,344,342,346,347,345,341,339,340,337,338,336,193,194,192,196,197,195,199,200,198,202,203,201,693,691,690,692,583,582,584,585,586,587,580,581,579,576,577,578,589,590,588,592,593,591,595,596,594,598,599,597,600,601,602,603,604,605,606,607,608,609,610,611,572,570,571,575,573,574,567,568,569,566,564,565,96,97,98,99,100,101,102,103,104,105,106,107,666,665,663,664,121,120,122,123,124,125,126,127,128,129,130,131,133,134,132,136,137,135,139,140,138,142,143,141,144,145,146,147,148,149,150,151,152,153,154,155,158,156,157,161,159,160,164,162,163,167,165,166,213,214,215,212,210,211,204,205,206,207,208,209,689,696,694,695,529,528,530,531,532,533,534,535,536,537,538,539,541,542,540,544,545,543,547,548,546,550,551,549,554,552,553,557,555,556,560,558,559,563,561,562,517,518,516,520,521,519,523,524,522,526,527,525,179,177,178,175,176,174,170,168,169,173,171,172,681,685,674,686,12,14,13,17,15,16,20,18,19,23,21,22,54,55,56,57,58,59,52,53,51,48,49,50,66,67,68,69,70,71,64,65,63,60,61,62,78,79,80,81,82,83,76,77,75,72,73,74,221,219,220,217,218,216,227,225,226,223,224,222,697,699,702,703,2,0,1,4,5,3,7,8,6,10,11,9,306,307,308,309,310,311,304,305,303,300,301,302,319,320,318,322,323,321,317,315,316,313,314,312,331,332,330,334,335,333,329,327,328,325,326,324,280,281,279,276,277,278,286,287,285,282,283,284,662,671,670,672,403,402,404,405,406,407,400,401,399,396,397,398,409,410,408,412,413,411,415,416,414,418,419,417,421,422,420,424,425,423,427,428,426,430,431,429,392,390,391,395,393,394,387,388,389,386,384,385,112,113,111,108,109,110,118,119,117,114,115,116,678,673,679,680 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#22cb8afe1ff0462b448663f4450c6ce0a1106142be9f7b23381e657feeb5c2cf, 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 15:34:18 · history