Equation 677 Database

← all  ·  ← by size  ·  ← size 381

Magma bd20aae59a84…

magma bd20aae59a84
Size
381
Isomorphism class hash
bd20aae59a848750cad8be77815f3dc472761228294a0fc4c7ab79aa4c598607
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 23:48:34
Display reorder
380,186,181,190,195,171,176,90,95,100,105,111,116,25,0,5,10,15,20,306,307,308,309,310,311,275,251,256,261,266,270,296,205,210,215,201,286,70,76,81,86,60,65,245,221,226,230,235,240,40,45,50,55,31,36,160,290,166,155,150,281,120,125,130,135,141,146,345,340,366,354,360,370,338,355,330,377,189,183,194,198,173,178,94,99,104,108,113,119,28,3,8,13,19,24,326,327,328,329,324,325,279,253,259,264,269,274,299,209,213,218,203,288,74,79,84,89,64,68,249,223,229,234,239,244,41,46,51,56,30,35,163,294,168,158,153,284,124,129,134,138,143,149,348,336,369,351,362,373,343,359,339,371,185,180,191,196,170,175,91,96,101,106,110,115,26,1,6,11,16,21,304,305,301,300,302,303,276,250,255,260,265,271,295,206,211,216,200,285,71,75,80,85,61,66,246,220,225,231,236,241,42,47,52,57,32,37,161,291,165,156,151,280,121,126,131,136,140,145,346,331,367,352,368,379,337,357,332,378,188,184,193,199,174,179,93,98,103,109,114,118,29,4,9,14,18,23,320,321,322,323,318,319,278,254,258,263,268,273,298,208,214,219,204,289,73,78,83,88,63,69,248,224,228,233,238,243,44,49,54,59,34,39,164,293,169,159,154,283,123,128,133,139,144,148,349,342,361,353,364,375,344,358,335,372,187,182,192,197,172,177,92,97,102,107,112,117,27,2,7,12,17,22,316,317,312,313,314,315,277,252,257,262,267,272,297,207,212,217,202,287,72,77,82,87,62,67,247,222,227,232,237,242,43,48,53,58,33,38,162,292,167,157,152,282,122,127,132,137,142,147,347,334,365,350,363,374,341,356,333,376 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#e7d843eeb4140ee4f2ae7f87ad1590cd2b2e584cf01474530a75f9f611790378, M = {76} 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 23:48:35 · history