Equation 677 Database

← all  ·  ← by size  ·  ← size 381

Magma 641f1a13ce48…

magma 641f1a13ce48
Size
381
Isomorphism class hash
641f1a13ce4816051be9a777eaaac140919865f970d525bb644a037880d740cf
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 23:21:49
Display reorder
380,14,24,4,102,112,122,52,57,67,152,132,142,194,204,209,214,316,312,314,179,189,164,174,274,254,264,234,244,224,92,32,77,82,47,87,27,97,9,284,107,117,72,62,137,147,219,315,313,184,269,279,229,239,37,42,19,127,292,157,199,317,169,259,249,297,287,376,352,368,356,336,347,342,330,369,373,12,22,2,104,114,124,54,59,69,154,134,144,191,200,205,210,325,327,329,176,186,160,171,272,252,262,230,240,220,94,34,79,84,49,89,29,99,7,282,109,119,74,64,139,149,215,324,328,181,267,277,225,235,39,44,17,129,294,159,195,326,166,257,245,299,289,379,354,364,358,339,349,344,334,362,371,13,23,3,101,110,120,51,55,65,151,131,140,193,203,208,213,304,301,302,178,188,163,173,273,253,263,233,243,223,90,31,76,81,45,86,26,95,8,283,105,115,70,60,135,145,218,303,300,183,268,278,228,238,36,41,18,125,290,156,198,305,168,258,248,296,286,377,350,365,355,335,345,340,331,360,372,10,21,1,103,113,123,53,58,68,153,133,143,190,201,206,211,308,310,306,175,185,161,170,271,250,261,231,241,221,93,33,78,83,48,88,28,98,5,280,108,118,73,63,138,148,216,307,311,180,266,276,226,236,38,43,15,128,293,158,196,309,165,256,246,298,288,378,353,366,357,338,348,343,333,367,370,11,20,0,100,111,121,50,56,66,150,130,141,192,202,207,212,319,321,323,177,187,162,172,270,251,260,232,242,222,91,30,75,80,46,85,25,96,6,281,106,116,71,61,136,146,217,322,318,182,265,275,227,237,35,40,16,126,291,155,197,320,167,255,247,295,285,375,351,363,359,337,346,341,332,361,374 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#4422b92082c5ba9f603861f57ee03bc11c9f901f0082cee83e1cd8bfe00bbd4d, 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 23:21:50 · history