Equation 677 Database

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Magma 05e5192d72b9…

magma 05e5192d72b9
Size
321
Isomorphism class hash
05e5192d72b95de376afa153813285a9d13a734145ce4c056a3b6654143b4a1e
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 23:04:04
Display reorder
300,158,157,156,160,161,159,163,164,162,166,167,165,18,19,20,21,22,23,16,17,15,12,13,14,226,227,225,222,223,224,217,218,216,220,221,219,204,205,206,207,208,209,210,211,212,213,214,215,267,268,269,266,264,265,273,274,275,272,270,271,301,313,308,310,87,89,88,85,86,84,95,93,94,91,92,90,104,102,103,107,105,106,99,100,101,98,96,97,111,112,113,110,108,109,117,118,119,116,114,115,125,123,124,121,122,120,131,129,130,127,128,126,74,72,73,77,75,76,80,78,79,83,81,82,317,320,318,319,33,35,34,31,32,30,26,24,25,29,27,28,231,232,233,230,228,229,237,238,239,236,234,235,37,38,36,40,41,39,43,44,42,46,47,45,170,168,169,173,171,172,176,174,175,179,177,178,276,277,278,279,280,281,282,283,284,285,286,287,304,314,306,309,297,299,298,295,296,294,290,288,289,293,291,292,135,136,137,134,132,133,141,142,143,140,138,139,188,186,187,191,189,190,183,184,185,182,180,181,53,51,52,49,50,48,59,57,58,55,56,54,242,240,241,245,243,244,248,246,247,251,249,250,303,316,307,312,197,196,195,192,193,194,202,203,201,198,199,200,258,259,260,261,262,263,256,257,255,252,253,254,63,64,65,62,60,61,69,70,71,68,66,67,3,4,5,2,1,0,9,10,11,8,6,7,150,151,152,153,154,155,148,149,147,144,145,146,302,315,305,311 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#f6a46900b44d5ece02211ebe9219e83165d75916b83af00bea786f1bcca6cac9, M = {62} 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 23:04:05 · history