Equation 677 Database

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Magma 5e68f78381d1…

magma 5e68f78381d1
Size
321
Isomorphism class hash
5e68f78381d186b9530fc628d347572bf9a78b3abd43f68cc3480af202130738
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 320) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-01 22:28:37
Display reorder
300,4,216,26,126,229,5,127,217,24,230,3,128,218,25,228,1,219,129,29,232,0,220,130,27,233,2,221,131,28,231,222,124,32,10,235,223,125,30,11,236,224,123,31,9,234,120,225,35,6,238,121,226,33,7,239,122,227,34,8,237,303,310,315,314,249,259,258,257,256,250,260,262,261,263,251,252,254,253,255,248,270,268,269,271,246,274,273,272,275,247,266,264,265,267,282,280,281,240,283,286,284,285,241,287,278,277,276,242,279,293,294,292,243,295,297,298,296,244,299,288,290,289,245,291,319,320,318,317,135,169,156,150,85,136,151,170,157,86,137,152,168,158,84,134,172,153,159,88,132,173,154,160,89,133,171,155,161,87,175,148,162,141,91,176,149,163,142,92,174,147,164,143,90,144,178,165,140,94,145,179,166,138,95,146,177,167,139,93,313,305,306,312,96,43,17,64,58,97,65,44,15,59,98,63,42,16,57,99,46,60,13,54,100,47,61,14,55,101,45,62,12,56,41,70,23,102,49,39,71,21,103,50,40,69,22,104,48,66,37,19,105,52,67,38,20,106,53,68,36,18,107,51,301,302,308,316,72,205,192,183,116,73,184,206,193,114,74,185,204,194,115,75,208,182,195,119,76,209,180,196,117,77,207,181,197,118,211,189,198,78,111,212,190,199,79,112,210,191,200,80,113,188,214,201,81,110,186,215,202,82,108,187,213,203,83,109,309,304,307,311 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 321 = 1 + 5*64, 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#48377dacddf39e37ac6c06158aa2a2d147d932b71f91ecfb6a61a025238f8f4a, M = {60} 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, 64): MacNeish's product over GF(64); GF(64) = F_2[x]/(x^6 + 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: 21.

last edited by qawbecrdtey at 2026-10-01 22:28:38 · history