Equation 677 Database

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Magma 21f1195f3388…

magma 21f1195f3388
Size
381
Isomorphism class hash
21f1195f33888658e92d89451f97c726c2cc77ec739e2b0611b54157b6d2cfca
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 23:25:43
Display reorder
380,262,257,267,272,277,282,52,49,48,294,50,51,54,287,55,56,57,53,197,202,207,212,217,222,60,61,62,63,58,59,312,313,314,315,316,317,65,66,67,68,69,64,135,136,132,299,133,134,73,74,75,70,71,72,187,192,167,172,177,182,245,227,237,251,232,240,338,335,340,370,361,369,346,355,376,354,261,256,266,271,276,281,157,158,154,293,155,156,143,292,144,145,146,147,196,201,206,211,216,221,149,150,151,152,153,148,325,327,329,318,320,323,161,162,163,164,159,160,8,9,10,296,6,7,139,140,141,142,137,138,185,190,165,170,175,180,247,225,235,250,230,242,331,330,341,365,360,374,347,351,377,359,260,255,265,270,275,280,101,102,103,289,99,100,77,288,78,79,80,76,195,200,205,210,215,220,83,84,85,86,81,82,309,310,311,306,307,308,88,89,90,91,92,87,4,5,0,295,2,3,96,97,98,93,94,95,186,191,166,171,176,181,246,226,236,253,231,241,337,336,342,372,364,371,348,357,375,356,264,259,269,274,279,284,30,31,32,285,28,29,1,286,33,34,35,22,199,204,209,214,219,224,38,39,40,41,36,37,324,326,328,319,321,322,43,44,45,46,47,42,25,26,27,298,23,24,16,17,18,19,20,21,189,194,169,174,179,184,249,229,239,254,234,244,339,334,344,366,363,368,349,350,379,353,263,258,268,273,278,283,129,130,131,291,127,128,118,290,119,120,116,117,198,203,208,213,218,223,124,125,126,121,122,123,300,302,303,304,305,301,107,108,109,104,105,106,11,12,13,297,14,15,115,110,111,112,113,114,188,193,168,173,178,183,248,228,238,252,233,243,332,333,343,367,362,373,345,352,378,358 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#50609e522fd5f79e53ac56beafcb5b424f2d261582798854b4ac2a2a84486b65, 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 23:25:43 · history