Equation 677 Database

← all  ·  ← by size  ·  ← size 705

Magma d8370ef8808d…

magma d8370ef8808d
Size
705
Isomorphism class hash
d8370ef8808dd37009fee418348b6b0f514641742ebc4ddca394201e982e32d5
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 19:07:51
Display reorder
660,504,511,505,500,237,531,238,524,525,520,239,491,484,485,480,431,236,424,425,422,234,452,448,450,449,235,471,463,465,464,228,631,624,625,622,229,651,644,645,642,602,230,611,604,605,551,231,544,545,542,565,571,232,564,562,591,233,584,585,582,686,699,688,690,510,515,508,512,44,535,42,530,528,532,43,495,490,488,492,435,47,430,428,432,45,459,458,456,445,46,475,470,468,472,39,635,630,628,632,40,655,650,648,652,612,41,615,610,608,555,38,550,548,552,568,575,36,570,572,595,37,590,588,592,691,694,689,695,51,210,400,316,22,211,23,52,401,317,21,212,53,399,315,213,18,50,396,312,19,214,48,397,313,20,215,49,398,314,13,208,57,406,322,14,209,58,407,323,321,12,207,59,405,204,16,56,402,318,403,205,17,54,319,206,15,55,404,320,666,678,662,668,135,352,296,163,263,353,261,136,294,164,262,351,137,295,162,348,259,134,299,166,260,349,132,297,167,258,350,133,298,165,254,358,141,291,161,252,359,142,292,159,160,253,357,143,293,354,257,140,290,157,288,355,255,138,158,356,256,139,289,156,663,664,676,671,516,501,507,514,97,521,98,536,527,534,96,481,496,487,494,420,100,436,427,434,101,443,447,444,446,99,461,476,467,474,103,621,636,627,634,104,640,656,647,654,614,102,601,616,607,541,106,556,547,554,567,560,107,576,574,580,105,596,587,594,700,703,698,702,518,517,519,513,127,537,128,538,539,533,126,497,498,499,493,437,130,438,439,433,131,440,441,442,453,129,478,477,479,473,125,638,637,639,633,123,657,658,659,653,613,124,618,617,619,557,121,558,559,553,579,577,122,578,573,598,120,597,599,593,692,701,687,697,509,503,502,506,153,523,154,529,522,526,155,483,489,482,486,423,152,429,421,426,150,455,457,454,451,151,462,469,460,466,144,623,629,620,626,145,643,649,641,646,606,146,603,609,600,543,147,549,540,546,561,563,148,569,566,583,149,589,581,586,696,704,685,693,199,86,328,117,6,84,7,200,329,118,8,85,198,327,119,89,9,202,324,116,10,87,203,325,114,11,88,201,326,115,4,92,197,334,108,5,90,195,335,109,110,3,91,196,333,95,1,193,330,111,331,93,0,194,112,94,2,192,332,113,680,667,670,679,175,280,273,388,246,281,247,176,274,389,248,279,174,275,387,276,249,178,272,384,250,277,179,270,385,251,278,177,271,386,244,286,173,264,394,245,287,171,265,395,393,243,285,172,266,282,240,169,267,390,268,283,241,170,391,284,242,168,269,392,675,681,684,661,364,304,62,223,32,305,30,365,60,224,31,303,363,61,222,300,35,360,65,226,33,301,361,63,227,34,302,362,64,225,27,310,370,68,221,28,311,371,66,219,220,29,309,369,67,306,26,366,71,217,69,307,24,367,218,308,25,368,70,216,683,672,673,665,412,376,74,340,181,377,182,413,72,341,180,375,411,73,339,372,184,408,77,336,185,373,409,75,337,183,374,410,76,338,187,382,418,80,346,188,383,419,78,347,345,186,381,417,79,378,190,414,83,342,81,379,191,415,343,380,189,416,82,344,669,677,682,674 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#87aba77d55a93960597d69a42bda986d959be94fa8d2c920629e2ba026b38a72, M = {60} in E, B = magma#9878faa9b07066f62fc077f7c99df5b1f6f079c61c0cd7e7f5bbdb9bc181adbc. 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 19:07:52 · history