Equation 677 Database

← all  ·  ← by size  ·  ← size 705

Magma 9fbe330ed9e3…

magma 9fbe330ed9e3
Size
705
Isomorphism class hash
9fbe330ed9e3a1f43f7afa86d8e9b4246111b7be83a5dd5a88163f16b9d21b08
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 18:23:29
Display reorder
660,19,192,388,103,339,193,101,20,386,340,191,102,18,387,338,195,22,384,106,335,196,23,385,104,336,194,21,383,105,337,17,394,190,109,345,15,392,188,107,346,16,393,189,108,344,390,13,186,112,341,391,14,187,110,342,389,12,185,111,343,663,670,672,662,361,229,294,8,222,227,6,359,295,223,228,7,360,293,221,232,364,297,11,225,230,362,298,9,226,231,363,296,10,224,367,292,235,3,220,365,290,233,4,218,366,291,234,5,219,288,370,238,2,216,289,368,236,1,217,287,369,237,0,215,689,690,685,686,55,411,155,583,517,412,584,53,156,518,410,582,54,157,516,407,58,158,579,513,408,56,159,580,514,409,57,160,581,515,61,153,417,589,523,59,154,418,590,524,60,152,416,588,522,149,64,413,585,519,150,62,414,586,520,151,63,415,587,521,668,671,665,669,249,469,303,571,459,470,572,250,304,460,468,570,248,302,461,465,245,299,567,462,466,246,300,568,463,467,247,301,569,464,240,309,475,577,457,241,310,476,578,458,239,308,474,576,456,305,243,471,573,453,306,244,472,574,454,307,242,473,575,455,676,683,678,674,252,435,493,315,375,436,316,253,494,376,434,314,251,492,374,431,255,489,311,371,432,256,490,312,372,433,254,491,313,373,258,499,441,321,381,259,500,442,322,382,257,498,440,320,380,495,261,437,317,377,496,262,438,318,378,497,260,439,319,379,664,661,666,667,75,559,143,529,405,560,530,76,144,406,558,528,74,145,404,555,71,146,525,401,556,72,147,526,402,557,73,148,527,403,66,141,565,535,396,67,142,566,536,397,65,140,564,534,395,137,69,561,531,399,138,70,562,532,400,139,68,563,533,398,694,695,696,693,26,443,452,595,36,634,635,24,632,633,444,594,25,451,37,446,29,448,591,39,447,27,449,592,40,445,28,450,593,38,32,653,652,655,654,30,657,656,659,658,31,649,648,651,650,637,35,636,639,638,641,33,640,643,642,644,34,645,647,646,703,704,701,702,266,200,600,552,323,201,553,267,601,324,202,554,268,599,325,199,265,596,551,326,197,263,597,549,327,198,264,598,550,328,272,606,629,628,329,273,607,631,630,330,274,605,627,626,331,602,271,620,621,332,603,269,623,622,333,604,270,625,624,334,697,700,699,698,100,541,612,174,134,542,175,98,613,135,540,173,99,611,136,537,96,608,177,133,538,97,609,178,131,539,95,610,176,132,91,618,547,180,125,89,619,548,181,126,90,617,546,179,127,614,94,543,183,128,615,92,544,184,129,616,93,545,182,130,682,673,681,684,204,49,354,423,281,47,424,205,355,282,48,422,203,353,283,52,207,357,419,284,50,208,358,420,285,51,206,356,421,286,210,352,44,429,279,211,350,45,430,280,209,351,46,428,278,348,213,43,425,275,349,214,41,426,276,347,212,42,427,277,680,677,679,675,85,122,481,165,505,123,166,83,482,506,124,164,84,480,504,121,88,477,161,501,119,86,478,162,502,120,87,479,163,503,80,487,113,171,511,81,488,114,172,512,82,486,115,170,510,483,79,116,167,507,484,77,117,168,508,485,78,118,169,509,688,692,691,687 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#7eb365a46a73bc671c535e7eab37a7fd590c6d5c6b4c14d45f700003c9150a2d, 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 18:23:30 · history