Equation 677 Database

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Magma ffacaf3b81ff…

magma ffacaf3b81ff
Size
381
Isomorphism class hash
ffacaf3b81ff0663d205d0b64db54e89dc1107edfde4f6328f9638a7bb59b3c8
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 23:43:15
Display reorder
380,287,237,232,222,227,217,72,77,80,87,92,282,152,157,162,167,172,177,267,277,262,252,257,247,302,301,300,305,303,304,242,46,47,45,43,44,112,117,107,97,102,291,36,37,272,0,1,212,187,192,182,202,207,197,137,147,142,132,122,127,297,42,41,39,40,38,367,337,357,362,332,372,347,342,351,376,286,236,230,221,226,216,70,75,81,86,90,280,151,156,161,165,170,176,266,276,261,251,255,246,314,312,313,317,315,316,240,19,20,18,16,17,110,115,106,95,100,290,2,3,271,4,5,210,185,190,180,201,206,196,136,145,141,130,121,125,295,34,33,31,32,30,366,335,355,361,331,370,346,340,350,375,289,239,234,224,229,219,74,79,83,88,93,283,153,158,163,168,173,178,268,278,263,254,259,249,318,319,320,321,322,323,244,65,66,64,63,67,113,118,108,98,103,293,68,69,274,13,12,214,189,194,184,204,209,199,138,148,143,133,123,128,299,62,61,59,60,58,369,339,359,363,334,373,349,343,353,378,288,238,233,223,228,218,73,78,82,89,94,284,154,159,164,169,174,179,269,279,264,253,258,248,327,328,329,324,325,326,243,56,57,53,54,55,114,119,109,99,104,294,48,49,273,10,11,213,186,191,181,200,205,195,139,149,144,134,124,129,298,51,50,14,52,15,368,338,358,364,330,374,348,344,354,379,285,235,231,220,225,215,71,76,84,85,91,281,150,155,160,166,171,175,265,275,260,250,256,245,310,311,309,307,308,306,241,21,22,23,24,25,111,116,105,96,101,292,28,29,270,26,27,211,188,193,183,203,208,198,135,146,140,131,120,126,296,35,6,7,8,9,365,336,356,360,333,371,345,341,352,377 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#c3f553b30d54716d9e2e87cb9ed350bbbf2e522a2867abba1f7ef649b9b0800a, M = {75} 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 23:43:16 · history