Equation 677 Database

← all  ·  ← by size  ·  ← size 705

Magma 8003064b2f39…

magma 8003064b2f39
Size
705
Isomorphism class hash
8003064b2f39adeb495e42687441b6ea7b68c71e672ad9c9ea563b55cd32ce6c
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 21:19:28
Display reorder
660,204,384,114,528,408,205,115,526,406,382,206,383,116,527,407,531,117,207,387,411,118,208,385,529,409,119,209,386,530,410,112,390,210,534,414,113,388,211,532,412,111,389,212,533,413,393,108,213,537,417,391,109,214,535,415,392,110,215,536,416,672,662,664,669,420,361,252,396,88,418,253,394,89,362,419,363,254,395,87,399,255,423,360,84,256,421,358,397,85,257,422,359,398,86,258,367,426,402,94,259,368,424,400,95,260,369,425,401,93,366,261,429,405,90,364,262,427,403,91,365,263,428,404,92,687,685,688,686,36,179,239,444,68,37,237,442,66,177,38,178,238,443,67,447,235,39,175,71,236,40,176,445,69,234,41,174,446,70,230,170,42,450,63,228,168,43,448,64,229,169,44,449,65,173,233,45,453,62,171,231,46,451,60,172,232,47,452,61,671,670,665,666,372,134,299,274,576,370,300,275,574,132,371,133,301,273,575,270,302,375,137,579,303,373,135,271,577,304,374,136,272,578,305,140,378,265,582,306,138,376,266,580,307,139,377,264,581,143,308,381,268,585,141,309,379,269,583,142,310,380,267,584,674,673,682,675,468,323,277,314,81,466,278,315,82,324,467,325,276,316,83,313,280,471,326,80,281,469,327,311,78,279,470,328,312,79,283,329,474,320,72,284,330,472,321,73,282,331,473,322,74,332,286,477,319,75,333,287,475,317,76,334,285,476,318,77,667,661,663,668,432,516,163,220,456,430,164,221,454,514,431,515,162,219,455,216,166,435,519,459,167,433,517,217,457,165,434,518,218,458,161,522,438,226,462,159,520,436,227,460,160,521,437,225,461,525,157,441,222,465,523,158,439,223,463,524,156,440,224,464,694,696,695,697,623,621,124,620,622,615,125,614,613,612,619,617,123,616,618,632,120,635,633,634,121,627,624,625,626,122,631,628,629,630,130,645,647,644,646,131,636,639,637,638,129,641,643,640,642,657,126,659,656,658,648,127,651,649,650,653,128,655,652,654,702,701,704,703,293,17,34,588,340,294,35,586,341,15,295,16,33,587,342,591,30,296,13,343,31,297,14,589,344,32,298,12,590,345,25,23,291,594,338,26,21,292,592,339,24,22,290,593,337,19,28,610,597,611,20,29,288,595,335,18,27,289,596,336,699,693,700,698,552,9,192,98,600,550,193,96,598,10,551,11,194,97,599,101,195,555,8,603,196,553,6,99,601,197,554,7,100,602,198,1,558,104,606,199,0,556,102,604,200,2,557,103,605,3,201,561,107,609,4,202,559,105,607,5,203,560,106,608,680,679,684,683,504,480,346,540,564,502,347,538,562,478,503,479,348,539,563,543,349,507,483,567,350,505,481,541,565,351,506,482,542,566,352,486,510,546,570,353,484,508,544,568,354,485,509,545,569,489,355,513,549,573,487,356,511,547,571,488,357,512,548,572,677,676,681,678,247,56,188,151,492,248,186,152,490,54,246,55,187,150,491,154,191,250,59,495,189,251,57,155,493,190,249,58,153,494,183,51,245,149,498,184,52,243,147,496,185,53,244,148,497,50,182,241,145,501,48,180,242,146,499,49,181,240,144,500,690,692,689,691 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#e6ff3ea71fab369083c7c0ebcc1e5818a214c988729d733a41fa2a4b44566c90, 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 21:19:29 · history