Equation 677 Database

← all  ·  ← by size  ·  ← size 705

Magma 66cd95315ec4…

magma 66cd95315ec4
Size
705
Isomorphism class hash
66cd95315ec4838db5d1a17212586fe359d6a28dbee56bb23db11c0a7f1a5e7d
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 16:36:09
Display reorder
704,497,374,488,475,486,495,476,372,487,373,496,474,493,491,377,478,494,489,375,479,492,490,376,477,483,380,473,503,484,378,471,501,485,379,472,502,383,482,469,499,381,480,470,500,382,481,468,498,506,504,505,509,507,508,512,510,514,515,513,511,660,663,662,661,174,108,163,151,164,175,152,109,162,110,176,150,177,166,111,154,178,167,112,155,179,165,113,153,161,114,149,172,159,115,147,173,160,116,148,171,117,157,145,168,118,158,146,169,119,156,144,170,140,138,139,143,141,142,135,136,133,134,132,137,691,689,688,690,537,402,526,555,527,538,556,403,525,404,539,557,536,522,405,554,534,523,406,552,535,524,407,553,517,400,561,528,518,401,562,529,516,399,563,530,396,520,560,531,397,521,558,532,398,519,559,533,546,547,548,549,550,551,544,545,542,540,541,543,671,669,668,670,201,45,180,221,181,202,219,46,182,47,203,220,200,183,44,217,198,184,42,218,199,185,43,216,186,36,227,192,187,37,225,193,188,38,226,194,39,189,223,195,40,190,224,196,41,191,222,197,210,211,212,213,214,215,208,209,206,204,205,207,678,677,676,679,257,19,242,231,240,255,232,20,241,18,256,233,253,245,22,230,254,243,23,228,252,244,21,229,248,17,237,263,246,15,238,261,247,16,239,262,13,251,236,259,14,249,234,260,12,250,235,258,266,264,265,269,267,268,272,270,274,275,273,271,666,665,664,667,658,659,657,656,649,650,648,651,653,655,654,652,642,640,643,641,646,644,647,645,638,636,639,637,621,623,620,622,613,615,612,614,617,619,616,618,635,632,633,634,627,624,625,626,631,628,629,630,389,387,388,385,386,384,395,393,390,391,392,394,692,694,695,693,68,49,104,85,102,66,86,50,103,48,67,84,71,107,52,88,69,105,53,89,70,106,51,87,99,55,91,63,100,56,92,64,101,54,90,65,58,98,94,62,59,96,95,60,57,97,93,61,76,77,75,72,73,74,82,83,80,78,79,81,700,702,703,701,296,31,285,317,286,294,315,32,287,30,295,316,299,284,34,313,297,282,35,314,298,283,33,312,276,29,323,291,277,27,321,292,278,28,322,293,25,279,319,290,26,280,320,288,24,281,318,289,305,303,304,301,302,300,311,309,306,307,308,310,696,698,699,697,438,4,429,466,430,439,467,5,431,3,440,465,441,428,1,462,442,426,0,463,443,427,2,464,420,10,457,436,421,11,458,437,422,9,456,435,6,423,460,432,7,424,461,433,8,425,459,434,445,446,444,448,449,447,451,452,453,454,455,450,675,673,672,674,331,124,369,348,370,332,349,125,371,123,330,350,334,368,120,351,335,366,121,352,333,367,122,353,360,130,354,329,361,131,355,327,362,129,356,328,126,363,357,325,127,364,358,326,128,365,359,324,343,344,342,346,347,345,341,339,336,337,338,340,680,681,683,682,598,410,586,574,587,599,575,408,585,409,597,573,594,582,413,570,595,583,411,571,596,584,412,572,577,416,565,589,578,414,566,590,576,415,564,588,419,580,568,592,417,581,569,593,418,579,567,591,609,610,611,608,606,607,600,601,605,603,604,602,684,687,686,685 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#35abc55380bad4d0eeaaa3ec3d1bddd8996633b3da151c70fe1eca862e930666, M = {60} in E, B = magma#ca58a4a9ddeee171fc40b5c556a5095e4a2c63eee13557dcdf190986f06d14c3. 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 16:36:11 · history