Equation 677 Database

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Magma 97e7e1e95a40…

magma 97e7e1e95a40
Size
705
Isomorphism class hash
97e7e1e95a40d730084c6efcdf8d047cd2b99ab3e96f88da1b12e95704519164
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 15:22:17
Display reorder
660,218,464,512,32,526,216,462,510,30,524,217,463,511,31,525,221,515,467,28,529,513,219,465,29,527,466,220,27,528,514,507,459,38,213,521,508,460,36,214,522,509,461,37,215,523,458,506,34,212,520,456,504,35,210,518,457,505,33,211,519,674,681,685,684,261,308,180,0,540,259,306,181,2,538,260,307,182,3,539,257,183,311,4,543,184,258,309,5,541,310,256,6,542,185,178,303,7,252,535,179,304,8,250,536,177,305,9,251,537,302,174,10,255,534,300,175,11,253,532,301,176,12,254,533,670,663,671,668,488,564,368,267,102,486,562,366,265,103,487,563,367,266,104,491,371,567,263,105,369,489,565,264,106,566,490,262,107,370,363,559,273,483,108,364,560,271,484,109,365,561,272,485,110,558,362,269,482,111,556,360,270,480,112,557,361,268,481,113,683,687,679,675,633,628,632,60,629,617,612,616,61,613,625,620,624,62,621,657,656,653,63,652,640,641,637,64,636,645,649,65,644,648,592,589,58,593,588,600,596,59,601,597,608,604,57,609,605,580,583,54,585,584,51,236,55,287,14,52,237,56,286,13,704,700,702,703,43,140,132,225,155,44,138,133,226,153,42,139,134,227,154,39,135,143,224,151,136,40,141,222,152,142,41,223,150,137,130,146,231,49,161,131,144,232,50,159,129,145,233,48,160,149,126,230,45,157,147,127,228,46,158,148,128,229,47,156,694,693,689,690,67,282,344,189,500,68,280,342,190,498,66,281,343,191,499,70,347,285,188,503,345,71,283,186,501,284,69,187,502,346,339,277,195,73,495,340,278,196,74,496,341,279,197,72,497,276,338,194,76,494,274,336,192,77,492,275,337,193,75,493,661,662,669,665,416,122,428,84,245,414,120,426,85,246,415,121,427,86,244,419,431,125,87,248,429,417,123,88,249,124,418,89,247,430,423,117,82,411,243,424,118,83,412,241,425,119,81,413,242,116,422,78,410,239,114,420,79,408,240,115,421,80,409,238,691,695,696,692,380,576,95,203,452,378,574,93,201,450,379,575,94,202,451,383,91,579,199,455,92,381,577,200,453,578,382,198,454,90,101,571,209,375,447,99,572,207,376,448,100,573,208,377,449,570,97,205,374,446,568,98,206,372,444,569,96,204,373,445,676,688,680,686,630,634,635,15,631,614,618,619,16,615,622,626,627,17,623,654,659,658,18,655,643,638,642,19,639,650,646,20,647,651,595,594,21,590,591,603,602,22,598,599,611,610,23,606,607,586,587,24,581,582,517,530,25,53,234,516,531,26,1,235,698,697,699,701,320,392,356,294,552,318,390,354,295,550,319,391,355,296,551,323,359,395,297,555,357,321,393,298,553,394,322,299,554,358,351,387,292,315,547,352,388,293,316,548,353,389,291,317,549,386,350,288,314,546,384,348,289,312,544,385,349,290,313,545,664,667,672,666,404,332,440,166,476,402,330,438,167,474,403,331,439,165,475,407,443,335,162,479,441,405,333,163,477,334,406,164,478,442,435,327,172,399,471,436,328,173,400,472,437,329,171,401,473,326,434,168,398,470,324,432,169,396,468,325,433,170,397,469,677,673,682,678 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#15e0002a5ecb0f8e7ea13fca6591bd645ffece494b3bd71abe8f3bbcdb21ed68, M = {60} in E, B = magma#abfd8e025ce71b705594dbbe1465dc1c7328d12d30e12d07906d7138f9d583bc. 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 15:22:18 · history