Equation 677 Database

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Magma 0e540179b3fc…

magma 0e540179b3fc
Size
511
Isomorphism class hash
0e540179b3fc721d8e37a388cb3951a69fbf8de0f072c5722f403c49c9d53875
Satisfies Equation 255
yes
Right-cancellative
no
Idempotent
yes
Fiber matrix
symmetric: no · normal: yes · rank: 496 (nullity 15) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-06 19:05:57
Display reorder
506,508,501,510,509,505,504,500,503,507,502,9,169,29,164,168,298,131,138,355,43,175,171,417,73,173,170,70,341,172,174,129,136,79,410,78,128,117,301,55,116,166,414,111,165,212,312,303,56,442,299,10,297,69,95,412,338,44,263,211,248,127,130,77,137,429,81,126,139,112,30,411,145,322,428,247,317,264,350,451,71,96,346,363,498,455,459,486,473,457,472,456,461,366,403,398,368,365,408,369,367,393,300,144,327,72,167,74,80,82,333,97,286,16,281,285,274,199,181,356,21,238,234,439,152,236,233,149,340,235,237,198,223,85,432,154,197,134,228,62,135,283,419,229,282,57,311,227,64,420,275,98,273,148,7,422,336,22,147,58,76,194,200,155,224,437,182,193,180,230,15,436,186,320,447,75,316,146,351,450,150,8,345,361,497,476,463,464,481,466,494,480,483,376,401,396,378,375,406,379,377,391,276,184,325,151,284,153,86,183,331,245,176,25,278,177,206,261,265,359,50,66,249,423,35,157,250,191,343,156,65,260,18,59,443,267,259,4,113,280,3,68,446,114,277,93,314,302,279,424,207,246,205,192,185,430,335,49,190,94,88,258,262,268,17,444,61,257,266,115,26,427,119,323,431,87,318,189,354,454,33,0,348,362,495,487,490,468,488,474,475,471,467,374,402,397,371,373,407,372,370,392,208,118,328,34,67,36,60,63,330,23,40,195,161,39,251,187,107,358,20,104,269,426,47,102,270,37,344,101,103,217,105,219,425,109,218,158,253,162,159,51,413,231,160,14,313,254,163,433,42,24,252,38,179,416,337,19,201,13,204,132,188,110,106,448,222,133,108,232,196,438,255,321,418,203,315,202,353,453,53,178,349,360,496,469,458,477,491,460,462,482,470,382,400,395,384,381,405,380,383,390,41,256,326,54,52,48,220,221,332,2,143,12,294,142,307,215,290,357,45,226,243,435,125,288,244,121,342,287,225,214,6,92,434,99,213,31,240,296,32,140,449,241,293,27,310,239,295,445,308,1,306,120,83,421,339,46,305,28,272,210,216,100,5,441,291,209,289,242,11,440,89,324,415,271,319,304,352,452,122,84,347,364,499,478,492,489,485,465,493,484,479,386,404,399,388,385,409,389,387,394,309,90,329,123,141,124,91,292,334 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 511 = 11 + 5*100, 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, 5, B) with E = magma#b62f6bf6777d544cbbb8fb51949dfaafd85d541fac79a383635a9c57a03e32e2, M = {100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110} in E, B = magma#e549b5f8492c9b6b5ad530e3aa4f39c6e23d08645ebd1b36a3c2de2a5a23bac5. 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(5, 100): MacNeish's product over GF(4) x GF(25); GF(4) = F_2[x]/(x^2 + x + 1), GF(25) = F_5[x]/(x^2 + 2); 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: 511.

last edited by qawbecrdtey at 2026-10-06 19:06:01 · history