Equation 677 Database

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Magma 9e77eeba5da3…

magma 9e77eeba5da3
Size
381
Isomorphism class hash
9e77eeba5da37cb533efe1273c81e3d7c3c0bab7e3fb08542cd973dabb613f9b
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 23:42:19
Display reorder
380,192,232,214,188,304,239,221,206,199,225,193,226,233,215,186,305,237,219,204,200,194,227,231,213,187,303,238,220,205,198,300,223,190,201,208,197,234,183,212,216,217,224,302,191,202,209,195,235,184,210,222,301,218,189,203,207,196,236,185,211,181,182,229,230,228,180,334,371,342,363,343,362,361,370,375,344,119,61,72,112,320,68,79,101,94,86,117,84,62,73,113,318,66,80,99,95,118,85,60,74,111,319,67,78,100,93,329,81,114,96,103,92,63,110,70,77,75,82,321,115,97,104,90,64,108,71,83,317,76,116,98,102,91,65,109,69,105,106,87,88,89,107,340,333,357,360,341,369,356,358,359,374,269,277,288,262,309,284,295,251,244,270,267,271,278,289,263,310,282,296,249,245,268,272,276,290,261,308,283,294,250,243,322,297,264,246,253,242,279,260,286,293,291,298,307,265,247,254,240,280,258,287,299,306,292,266,248,252,241,281,259,285,255,256,274,275,273,257,350,348,372,366,367,365,349,337,373,379,163,137,148,156,313,141,123,174,170,130,164,131,135,149,157,311,142,124,175,168,162,129,136,147,158,312,143,125,176,169,316,128,161,172,179,165,139,154,146,121,122,126,314,159,173,177,166,140,155,144,127,315,120,160,171,178,167,138,153,145,152,150,134,132,133,151,346,378,345,376,335,364,336,338,377,347,27,7,46,20,325,0,50,53,34,8,28,9,5,44,21,323,59,51,54,32,26,10,6,45,22,324,1,52,55,33,328,58,25,36,40,29,4,18,41,48,49,56,326,23,37,38,30,2,19,42,57,327,47,24,35,39,31,3,17,43,16,14,12,13,11,15,352,330,332,355,354,331,353,351,339,368 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#c1c980e842b9e3e1b607a735e63be15f744bf765a2bfe5421392930b15ca8a7a, 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 23:42:19 · history