Equation 677 Database

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Magma 76b5f93fa1a5…

magma 76b5f93fa1a5
Size
381
Isomorphism class hash
76b5f93fa1a5b75b81c127e88e79c76027754f8605620c631c28c695ce805d21
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 23:46:03
Display reorder
380,314,313,315,316,311,312,285,291,296,272,275,280,37,38,39,40,41,36,206,180,186,191,196,201,55,56,57,58,59,54,266,240,245,250,255,260,47,42,43,44,45,46,32,33,34,35,30,31,49,50,51,52,53,48,216,221,226,231,236,210,150,171,155,161,166,176,361,354,344,343,337,370,339,375,365,356,304,303,305,301,300,302,287,292,297,273,277,282,96,97,98,99,100,101,207,182,187,192,197,202,118,119,114,115,116,117,267,242,247,252,257,262,102,103,104,105,106,107,93,94,95,90,91,92,110,111,112,113,108,109,217,222,227,232,237,212,152,172,157,162,167,177,362,351,348,346,333,374,347,377,367,357,308,307,309,310,329,306,286,290,295,271,276,281,146,147,148,149,144,145,205,181,185,190,195,200,134,135,136,137,132,133,265,241,246,251,256,261,122,123,124,125,120,121,139,140,141,142,143,138,130,131,126,127,128,129,215,220,225,230,235,211,151,170,156,160,165,175,360,352,334,330,332,371,336,376,369,359,317,322,318,319,320,321,289,294,299,274,278,284,88,89,84,85,86,87,209,184,189,194,199,204,75,76,77,72,73,74,269,244,249,254,259,264,61,62,63,64,65,60,82,83,78,79,80,81,69,70,71,66,67,68,219,224,229,234,239,214,154,174,159,164,169,179,364,353,338,349,331,373,345,379,368,358,326,325,327,328,323,324,288,293,298,270,279,283,1,0,2,3,4,5,208,183,188,193,198,203,11,6,7,8,9,10,268,243,248,253,258,263,21,22,23,18,19,20,14,15,16,17,12,13,29,24,25,26,27,28,218,223,228,233,238,213,153,173,158,163,168,178,363,350,340,342,335,372,341,378,366,355 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#dc50bff4268d4e886a12bccb100fd4b53117610e2c07e48d4c792db14c6c3b47, M = {67} 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 23:46:04 · history