Equation 677 Database

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Magma d8fe64dfe124…

magma d8fe64dfe124
Size
321
Isomorphism class hash
d8fe64dfe12498f97b6cf1e06122f3abbbf362b70924fc7910a1804f8e61f288
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 22:27:32
Display reorder
300,41,152,133,19,43,42,153,17,134,44,18,154,40,135,45,155,38,15,227,210,156,39,16,136,211,231,240,237,137,46,150,168,131,13,47,151,169,132,14,48,149,170,130,12,49,147,167,128,11,50,230,234,129,10,51,148,235,226,236,241,314,301,312,315,277,276,279,176,278,281,280,174,283,282,175,284,285,287,286,288,289,172,291,290,292,293,173,295,294,296,297,171,299,298,269,268,270,182,271,273,272,274,180,275,264,265,266,181,267,253,252,254,178,255,257,256,258,179,259,261,260,262,177,263,318,319,317,320,103,58,122,89,244,246,212,220,123,75,90,59,104,124,217,213,105,91,125,76,60,106,92,126,77,61,107,93,127,78,56,101,120,94,73,57,102,121,95,74,55,100,119,96,72,52,98,117,221,216,53,99,118,97,71,54,222,225,245,243,308,305,303,310,188,21,161,35,141,189,22,36,162,142,37,20,190,163,143,24,191,34,164,144,25,192,32,165,145,23,193,33,166,146,27,186,160,208,140,206,187,233,29,229,26,185,159,30,139,28,183,157,209,248,207,249,232,239,228,238,184,158,31,138,316,311,302,313,83,198,65,0,111,84,199,2,66,112,1,197,85,67,113,194,86,4,68,114,195,87,5,69,115,196,88,3,70,116,202,81,63,7,109,203,82,64,8,110,201,219,215,6,224,200,79,214,205,247,251,218,242,204,223,250,80,62,9,108,306,309,307,304 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#368900d303714df43b3718b8680935166fd1150994cfe143b7c0fba0a5b985be, 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 22:27:33 · history