Equation 677 Database

← all  ·  ← by size  ·  ← size 705

Magma dc1bd1a5a09e…

magma dc1bd1a5a09e
Size
705
Isomorphism class hash
dc1bd1a5a09e22003627464090bd4cce09325566f005f5ef865cd779e9f06f72
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 19:50:39
Display reorder
660,253,272,410,194,247,411,254,195,248,273,409,271,255,193,249,268,406,252,190,246,269,407,250,191,244,270,408,251,192,245,263,416,200,259,238,264,417,201,260,239,262,415,199,261,240,412,266,196,258,241,413,267,197,256,242,414,265,198,257,243,668,661,663,672,306,624,45,132,565,46,304,130,566,625,47,623,305,131,564,620,44,309,135,561,621,42,307,133,562,622,43,308,134,563,630,36,138,301,571,631,37,136,302,572,629,38,137,303,570,39,626,141,300,567,40,627,139,298,568,41,628,140,299,569,688,685,689,691,601,530,157,83,20,158,602,81,18,531,159,529,600,82,19,526,156,597,79,23,527,154,598,80,21,528,155,599,78,22,536,163,74,607,15,537,164,72,608,16,535,165,73,606,17,162,532,77,603,14,160,533,75,604,12,161,534,76,605,13,669,662,665,666,328,314,398,25,589,399,329,26,590,315,397,313,330,24,588,310,394,331,28,585,311,395,332,29,586,312,396,333,27,587,320,404,31,326,595,321,405,32,327,596,319,403,30,325,594,400,316,34,322,591,401,317,35,323,592,402,318,33,324,593,673,678,682,675,434,212,636,345,219,637,435,343,217,213,635,211,433,344,218,208,632,430,341,215,209,633,431,342,216,210,634,432,340,214,203,642,336,440,225,204,643,334,441,223,202,641,335,439,224,638,206,339,436,221,639,207,337,437,222,640,205,338,438,220,664,671,667,670,542,49,60,153,422,61,543,151,423,50,62,48,541,152,421,52,63,538,149,418,53,64,539,150,419,51,65,540,148,420,55,66,144,548,428,56,67,142,549,429,54,68,143,547,427,69,58,147,544,424,70,59,145,545,425,71,57,146,546,426,699,698,694,693,613,126,98,109,554,99,614,107,555,124,97,125,612,108,553,129,101,609,112,550,127,102,610,110,551,128,100,611,111,552,119,96,115,619,560,659,657,113,658,656,123,103,114,618,559,105,120,118,615,556,106,121,116,616,557,104,122,117,617,558,704,703,701,702,470,518,346,372,494,347,471,370,495,519,348,517,469,371,493,514,349,466,375,490,515,350,467,373,491,516,351,468,374,492,524,352,378,476,500,525,353,376,477,501,523,354,377,475,499,355,520,381,472,496,356,521,379,473,497,357,522,380,474,498,695,700,696,697,290,183,506,237,283,507,291,235,284,181,505,182,289,236,285,179,502,286,233,282,180,503,287,234,280,178,504,288,232,281,189,512,228,296,274,187,513,226,297,275,188,511,227,295,276,508,185,231,292,277,509,186,229,293,278,510,184,230,294,279,674,679,680,684,362,577,648,5,386,649,363,3,387,578,647,576,361,4,385,573,644,358,0,382,574,645,359,2,383,575,646,360,1,384,583,654,11,368,392,584,655,9,369,393,582,653,10,367,391,650,579,7,364,388,651,580,8,365,389,652,581,6,366,390,676,683,677,681,458,92,482,166,452,483,459,167,453,90,481,91,457,168,451,95,478,454,169,448,93,479,455,170,449,94,480,456,171,450,87,488,172,464,443,88,489,173,465,444,89,487,174,463,442,484,86,175,460,446,485,84,176,461,447,486,85,177,462,445,686,687,692,690 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#b0c577ef9e4c05d7925e972279aa7c10376825c460b06aa55c85bf856c0bbca9, 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 19:50:40 · history