Equation 677 Database

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Magma 8e996c8d8bf4…

magma 8e996c8d8bf4
Size
381
Isomorphism class hash
8e996c8d8bf4350281574290147fccca147d169eb46e02a47c7836b7a0f5c870
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 380) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-01 23:43:33
Display reorder
380,241,291,277,284,255,248,298,304,270,262,242,292,278,263,285,256,249,299,300,271,243,293,279,258,286,257,250,294,302,272,244,288,280,259,287,252,251,295,303,273,245,289,281,260,282,253,246,296,301,274,261,290,240,276,283,254,247,297,310,275,268,264,265,266,267,269,354,356,353,373,357,335,375,374,334,355,146,132,124,131,160,153,139,319,177,167,147,133,125,162,126,161,154,140,321,178,148,134,120,163,127,156,155,141,323,179,149,135,121,164,128,157,150,142,325,174,144,136,122,165,129,158,151,143,326,175,166,137,145,123,130,159,152,138,328,176,168,170,171,172,173,169,347,341,346,370,369,342,345,344,343,330,187,237,223,230,201,194,180,314,216,208,188,238,224,209,231,202,195,181,315,217,189,239,225,204,232,203,196,182,316,218,190,234,226,205,233,198,197,183,311,219,191,235,227,206,228,199,192,184,312,220,207,236,186,222,229,200,193,185,313,221,214,210,211,212,213,215,333,351,352,348,372,350,332,349,331,371,13,5,49,56,27,20,6,322,42,34,14,1,50,35,57,28,21,7,324,43,15,0,51,30,58,29,22,8,327,44,16,2,52,31,59,24,23,9,329,45,17,3,53,32,54,25,18,10,318,46,33,4,12,48,55,26,19,11,320,47,40,36,37,38,39,41,359,378,376,360,336,362,358,361,377,363,99,85,77,78,113,106,92,309,70,114,100,86,72,115,79,108,107,93,306,71,101,87,73,116,80,109,102,94,307,66,96,88,74,117,81,110,103,95,308,67,97,89,75,118,82,111,104,90,305,68,119,84,98,76,83,112,105,91,317,69,62,64,65,60,61,63,364,367,379,337,368,365,340,339,338,366 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 381 = 1 + 5*76, 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#ca8e8dba8adc6702e3d8ee12eca6bf29113521fc49a0cbc215f184f3ae4bad35, M = {66} 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, 76): MacNeish's product over GF(4) x GF(19); GF(4) = F_2[x]/(x^2 + 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: 51.

last edited by qawbecrdtey at 2026-10-01 23:43:34 · history