Equation 677 Database

← all  ·  ← by size  ·  ← size 705

Magma fa464c842274…

magma fa464c842274
Size
705
Isomorphism class hash
fa464c842274a68c168db6965a4f85e0a8ce3eba4e259fdde1a38ef005ad1dfa
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 17:31:00
Display reorder
660,406,55,400,334,131,407,129,56,401,335,54,130,405,399,333,402,58,127,396,330,403,59,128,397,331,404,57,126,398,332,61,412,137,391,340,62,413,135,392,341,390,60,411,136,339,64,408,133,394,336,65,409,134,395,337,63,410,132,393,338,684,675,686,676,182,159,87,508,228,180,229,160,88,509,161,230,181,89,507,185,158,231,86,504,183,156,232,84,505,184,157,233,85,506,150,177,226,78,514,151,178,227,79,515,80,152,179,225,513,153,176,222,81,510,154,174,223,82,511,155,175,224,83,512,666,668,661,670,544,460,496,242,34,545,35,461,497,240,459,33,543,495,241,540,456,30,492,245,541,457,31,493,243,542,458,32,494,244,466,550,40,502,237,467,551,41,503,238,501,465,549,39,239,462,546,36,498,236,463,547,37,499,234,464,548,38,500,235,679,674,678,681,454,14,363,388,196,455,197,12,364,389,13,195,453,365,387,450,17,192,362,384,451,15,193,360,385,452,16,194,361,386,647,649,187,645,648,655,657,188,653,656,636,639,641,186,640,613,614,190,616,617,623,625,191,620,624,631,633,189,629,632,703,699,697,704,520,322,376,472,120,521,121,323,377,473,321,122,519,375,471,516,318,123,372,468,517,319,124,373,469,518,320,125,374,470,328,526,118,382,478,329,527,119,383,479,381,327,525,117,477,324,522,114,378,474,325,523,115,379,475,326,524,116,380,476,691,692,690,693,90,484,532,442,254,91,252,485,533,443,483,253,92,531,441,93,480,257,528,438,94,481,255,529,439,95,482,256,530,440,490,96,249,538,448,491,97,250,539,449,537,489,98,251,447,486,99,248,534,444,487,100,246,535,445,488,101,247,536,446,669,663,665,664,299,20,292,278,76,297,77,18,293,276,19,75,298,291,277,295,23,72,288,281,296,21,73,289,279,294,22,74,290,280,26,305,67,283,273,24,303,68,284,274,282,25,304,66,275,29,301,70,286,272,27,302,71,287,270,28,300,69,285,271,694,695,696,689,310,586,568,604,45,311,46,587,569,605,585,47,309,567,603,306,582,44,564,600,307,583,42,565,601,308,584,43,566,602,592,316,51,574,610,593,317,52,575,611,573,591,315,53,609,588,312,50,570,606,589,313,48,571,607,590,314,49,572,608,683,688,685,673,359,598,580,368,352,357,353,599,581,366,597,351,358,579,367,355,594,348,576,371,356,595,349,577,369,354,596,350,578,370,651,644,343,650,646,659,652,344,658,654,642,643,637,342,638,619,618,346,615,612,627,621,347,626,622,635,628,345,634,630,701,698,702,700,221,140,204,418,166,219,167,138,205,419,139,165,220,206,417,217,143,162,207,414,218,141,163,208,415,216,142,164,209,416,146,212,172,202,424,144,210,173,203,425,201,145,211,171,423,149,215,168,198,420,147,213,169,199,421,148,214,170,200,422,672,662,671,667,262,109,430,556,5,263,3,110,431,557,108,4,261,429,555,258,112,0,426,552,259,113,2,427,553,260,111,1,428,554,107,268,11,436,562,105,269,9,437,563,435,106,267,10,561,103,264,7,432,558,104,265,8,433,559,102,266,6,434,560,677,682,680,687 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#58666f8071d01f531e6f0c3147dedbb33da52b01b6615c3c73eb980e964d7179, 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 17:31:02 · history