Equation 677 Database

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Magma da7f784d2ae9…

magma da7f784d2ae9
Size
705
Isomorphism class hash
da7f784d2ae9e26f25ab4570921482d2fcae2943b830856dc09dcf6943e5432a
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 18:14:59
Display reorder
660,172,528,504,543,480,173,505,544,481,529,171,530,506,545,482,503,168,527,542,479,169,501,525,540,477,170,502,526,541,478,534,163,495,519,471,164,496,520,535,472,162,497,521,536,473,498,166,522,537,474,499,167,523,538,475,500,165,524,539,476,680,685,684,682,41,114,158,441,366,39,156,442,367,115,40,116,157,443,368,161,44,117,440,365,42,159,118,438,363,43,160,119,439,364,432,47,153,120,357,45,154,121,433,358,46,155,122,434,359,152,50,123,435,360,150,48,124,436,361,151,49,125,437,362,662,665,670,666,13,330,561,405,65,14,562,406,63,331,12,332,563,407,64,560,9,329,404,68,10,558,327,402,66,11,559,328,403,67,396,4,552,321,71,5,553,322,397,69,3,554,323,398,70,555,7,324,399,74,556,8,325,400,72,557,6,326,401,73,687,678,675,686,269,641,638,642,637,267,646,650,644,649,268,657,654,658,652,630,265,633,634,628,266,614,617,618,612,264,622,625,626,620,546,260,271,531,87,258,272,532,547,88,259,270,533,548,89,589,263,591,593,592,598,261,601,602,597,604,262,609,610,605,703,700,704,698,143,182,417,453,295,141,418,454,296,180,142,181,419,455,294,416,139,185,452,291,140,414,183,450,292,138,415,184,451,293,444,149,408,177,286,147,409,178,445,287,148,410,179,446,285,411,145,176,447,289,412,146,174,448,290,413,144,175,449,288,694,692,689,690,79,239,248,573,468,80,246,574,469,237,78,238,247,575,470,251,75,235,572,467,76,249,236,570,465,77,250,234,571,466,564,85,254,245,459,86,252,243,565,460,84,253,244,566,461,257,81,241,567,462,255,82,242,568,463,256,83,240,569,464,667,672,661,664,111,51,429,209,211,112,430,207,212,52,113,53,431,208,210,428,110,54,205,214,108,426,55,206,215,109,427,56,204,213,200,102,420,57,217,103,421,58,198,218,104,422,59,199,216,423,105,60,203,220,424,106,61,201,221,425,107,62,202,219,695,693,696,691,222,516,342,585,492,223,343,586,493,517,224,518,344,587,494,341,225,515,584,491,226,339,513,582,489,227,340,514,583,490,576,228,333,507,483,229,334,508,577,484,230,335,509,578,485,336,231,510,579,486,337,232,511,580,487,338,233,512,581,488,681,688,683,676,37,643,640,636,639,38,648,645,647,651,36,659,656,653,655,632,33,635,629,631,34,616,619,613,615,35,624,627,621,623,2,28,458,549,369,29,456,550,1,370,27,457,551,0,371,594,31,595,588,590,600,32,603,596,599,608,30,611,606,607,697,702,701,699,282,393,136,26,382,283,137,24,383,394,284,395,135,25,381,132,281,392,22,378,279,133,390,23,379,280,134,391,21,380,17,273,127,384,373,274,128,385,15,374,275,126,386,16,372,130,276,387,20,376,131,277,388,18,377,129,278,389,19,375,668,671,663,669,93,354,303,318,197,94,304,319,195,355,95,356,305,320,196,306,92,353,317,193,90,307,351,315,194,91,308,352,316,192,309,99,301,345,188,100,302,346,310,186,101,300,347,311,187,297,98,348,312,191,298,96,349,313,189,299,97,350,314,190,674,673,677,679 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#6f4d58a1f1a96be51a4fbe5ecc6c97c30dc38acf270b654112619a91916a19da, 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 18:15:00 · history