Equation 677 Database

← all  ·  ← by size  ·  ← size 381

Magma bf4ccb698b0f…

magma bf4ccb698b0f
Size
381
Isomorphism class hash
bf4ccb698b0fc5b63d885fe2d9f603d02bf75fcc801fd788eba5437d247f943d
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 23:25:54
Display reorder
380,142,141,143,138,139,140,127,128,129,130,131,126,314,315,316,317,312,313,134,135,136,137,132,133,148,149,144,145,146,147,157,162,167,172,177,152,297,272,277,282,287,292,120,121,122,123,124,125,262,267,242,247,252,257,212,217,222,227,232,237,187,197,207,192,202,182,339,368,353,354,338,357,360,341,376,370,76,75,77,72,73,74,89,84,85,86,87,88,305,301,300,302,303,304,68,69,70,71,66,67,82,83,78,79,80,81,159,164,169,173,179,154,299,273,278,284,289,294,1,0,2,3,4,5,263,269,243,248,253,258,213,218,223,228,233,239,189,198,208,194,203,183,340,367,330,349,350,355,364,345,379,374,43,42,44,45,46,47,61,62,63,64,65,60,318,319,320,321,322,323,39,40,41,36,37,38,53,48,49,50,51,52,155,160,165,170,176,150,296,270,276,281,286,291,54,55,56,57,58,59,261,266,240,245,250,256,210,215,220,226,231,236,186,196,206,191,201,180,335,365,331,342,348,359,361,343,375,371,112,111,113,108,109,110,97,98,99,100,101,96,311,306,307,308,309,310,104,105,106,107,102,103,118,119,114,115,116,117,158,163,168,174,178,153,298,274,279,283,288,293,90,91,92,93,94,95,264,268,244,249,254,259,214,219,224,229,234,238,188,199,209,193,204,184,333,369,351,352,334,358,363,332,378,373,20,19,21,22,23,18,11,6,7,8,9,10,324,325,326,327,328,329,13,14,15,16,17,12,27,28,29,24,25,26,156,161,166,171,175,151,295,271,275,280,285,290,32,33,34,35,30,31,260,265,241,246,251,255,211,216,221,225,230,235,185,195,205,190,200,181,344,366,346,347,337,356,362,336,377,372 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 = {70} 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 23:25:55 · history