Equation 677 Database

← all  ·  ← by size  ·  ← size 381

Magma efc68ece29af…

magma efc68ece29af
Size
381
Isomorphism class hash
efc68ece29afe71ead7e4eb0c009e660d2eb2a93ac49066f5b296637877f2b41
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 23:28:54
Display reorder
380,323,322,321,319,320,318,203,193,198,188,178,183,38,273,43,48,53,58,88,93,283,98,103,108,33,22,28,267,13,18,208,213,218,223,228,233,123,113,118,288,7,6,258,263,253,240,248,236,63,68,73,78,83,278,158,153,298,173,163,168,143,293,148,128,133,138,363,333,358,347,373,368,343,338,353,378,301,302,300,305,303,304,200,191,196,186,175,181,35,271,41,46,50,55,86,91,280,95,101,106,30,20,25,266,12,17,206,210,215,221,225,230,121,110,116,285,0,2,256,260,251,243,247,237,61,65,70,75,80,276,155,152,297,170,160,165,142,292,147,125,130,136,362,330,355,349,370,367,341,337,350,377,314,313,312,316,317,315,201,190,195,185,176,180,37,272,40,45,51,56,85,90,281,96,100,105,31,24,26,265,11,16,205,211,216,220,226,231,122,112,117,287,4,5,255,261,250,242,246,238,60,66,71,76,81,275,157,151,295,171,161,167,141,290,145,127,132,137,360,331,357,346,371,366,342,335,351,375,308,307,306,310,311,309,202,192,197,187,177,182,36,270,42,47,52,57,87,92,282,97,102,107,32,21,27,268,10,15,207,212,217,222,227,232,120,111,115,286,3,1,257,262,252,241,245,235,62,67,72,77,82,277,156,150,296,172,162,166,140,291,146,126,131,135,361,332,356,345,372,365,340,336,352,376,325,324,326,327,328,329,204,194,199,189,179,184,39,274,44,49,54,59,89,94,284,99,104,109,34,23,29,269,14,19,209,214,219,224,229,234,124,114,119,289,9,8,259,264,254,244,249,239,64,69,74,79,84,279,159,154,299,174,164,169,144,294,149,129,134,139,364,334,359,348,374,369,344,339,354,379 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#5a9d04a9c7b116e670149859ec35e9ea984c3e29c9284ef9fa55ee11860b9239, M = {72} 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 23:28:55 · history