Equation 677 Database

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Magma 51cde64c5b52…

magma 51cde64c5b52
Size
321
Isomorphism class hash
51cde64c5b52ccbbc32dec54b882d235bd2cbb41a8f027ba718a8278df75d1d1
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 23:04:44
Display reorder
300,171,34,151,28,161,169,32,159,149,29,170,33,160,150,27,173,36,163,229,205,172,35,162,152,236,248,206,231,153,30,39,156,146,166,26,37,157,147,167,24,38,158,148,168,25,155,40,145,165,22,230,207,144,164,23,154,238,247,232,204,312,315,311,310,287,7,284,285,286,279,8,278,277,276,283,6,282,281,280,299,10,298,296,297,291,11,290,289,288,295,9,294,293,292,5,266,264,267,265,3,270,268,271,269,4,274,272,275,273,262,0,261,263,260,254,2,253,255,252,258,1,257,259,256,319,318,317,320,102,78,130,110,228,221,241,246,128,109,101,79,140,129,225,222,80,143,133,113,103,81,141,131,111,104,82,142,132,112,83,137,125,98,106,84,138,126,99,107,85,139,127,100,108,136,86,124,220,224,134,87,123,97,105,135,242,245,219,223,308,305,304,309,93,74,190,55,180,91,72,178,188,53,92,73,179,189,54,96,77,183,193,58,94,75,181,191,56,95,76,182,192,57,70,175,186,218,51,216,176,235,89,212,71,177,187,90,52,174,69,185,217,239,233,240,234,243,211,249,68,184,88,50,316,313,301,314,199,21,65,119,42,197,19,43,66,117,198,20,41,67,118,195,17,45,64,122,196,18,46,62,120,194,16,44,63,121,12,47,59,203,115,13,48,60,201,116,14,208,213,202,227,49,15,214,251,226,210,237,215,250,244,209,31,61,200,114,302,307,303,306 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#fd86fc294900b5ccb814b44936109aa3958b6cd4f65ecf12bfe08854715a531f, 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 23:04:45 · history