Equation 677 Database

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Magma bf7981b1b914…

magma bf7981b1b914
Size
705
Isomorphism class hash
bf7981b1b91461f7d8f27be72fb1ab9a538ef7c135f63e8bc753d858c86e0b89
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 15:11:08
Display reorder
660,373,44,2,429,537,374,538,42,1,430,372,536,43,0,428,540,47,376,5,432,377,541,45,3,433,539,46,375,4,431,39,379,543,8,435,40,380,544,6,436,41,378,542,7,434,382,38,546,11,438,383,36,547,9,439,381,37,545,10,437,674,676,673,682,282,181,303,301,266,283,267,179,304,299,281,268,180,302,300,269,177,278,306,297,279,270,178,307,298,271,176,280,305,296,172,288,272,309,292,170,289,273,310,290,171,287,274,308,291,284,175,275,312,295,285,173,276,313,293,286,174,277,311,294,670,665,672,661,193,315,441,513,561,191,562,316,442,514,192,560,314,440,512,564,318,189,444,516,190,565,319,445,517,563,317,188,443,515,321,184,567,447,519,322,182,568,448,520,320,183,566,446,518,187,324,570,450,522,185,325,571,451,523,186,323,569,449,521,677,680,685,683,346,55,69,116,385,347,386,56,67,117,345,384,57,68,118,388,54,342,65,119,343,389,52,66,120,387,53,344,64,121,61,339,391,73,122,62,340,392,71,123,63,338,390,72,124,646,60,647,648,649,657,58,658,652,654,341,59,393,70,125,704,700,703,697,367,220,465,525,573,368,574,218,466,526,366,572,219,464,524,576,223,370,468,528,371,577,221,469,529,575,222,369,467,527,226,365,579,471,531,224,363,580,472,532,225,364,578,470,530,361,229,582,474,534,362,227,583,475,535,360,228,581,473,533,691,692,689,694,253,195,328,501,232,251,230,196,326,502,252,231,194,327,500,235,198,249,331,504,250,233,199,329,505,234,197,248,330,503,201,244,238,334,507,202,242,236,332,508,200,243,237,333,506,247,204,241,337,510,245,205,239,335,511,246,203,240,336,509,668,664,666,667,23,132,213,549,115,21,113,133,214,550,22,114,134,212,548,111,135,19,216,552,20,112,136,217,553,110,137,18,215,551,130,14,106,211,555,131,12,104,209,556,129,13,105,210,554,17,126,109,207,558,15,127,107,208,559,16,128,108,206,557,695,693,696,690,597,86,453,633,33,598,34,87,454,634,596,35,88,452,632,32,89,600,456,636,601,30,90,457,637,31,91,599,455,635,84,603,24,459,639,85,604,25,460,640,83,602,26,458,638,606,80,27,462,642,607,81,28,463,643,605,82,29,461,641,678,688,686,681,78,149,152,164,419,79,420,147,150,165,77,418,148,151,166,422,145,74,155,167,75,423,146,153,168,421,144,76,154,169,140,49,425,158,162,138,50,426,156,163,139,51,424,157,161,650,143,651,644,645,653,141,659,655,656,48,142,427,159,160,698,702,701,699,489,258,407,621,355,490,356,259,408,622,488,354,257,406,620,358,254,492,410,624,493,359,255,411,625,357,256,491,409,623,264,495,353,413,627,265,496,351,414,628,263,494,352,412,626,498,260,349,416,630,499,261,350,417,631,497,262,348,415,629,662,671,663,669,477,99,395,585,609,478,610,100,396,586,476,608,98,394,584,612,102,480,398,588,481,613,103,399,589,611,101,479,397,587,97,483,615,401,591,95,484,616,402,592,96,482,614,400,590,486,93,618,404,594,487,94,619,405,595,485,92,617,403,593,675,684,679,687 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#07e8f68f5124a8e3a0938e8678de1c72ed7349b338061e203d5db711c48e18fa, 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 15:11:11 · history