Equation 677 Database

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Magma 7ee361b97eae…

magma 7ee361b97eae
Size
321
Isomorphism class hash
7ee361b97eae8705e9cbacfe84b2c019db89eddb525e6f8550738e925b981cec
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 22:26:50
Display reorder
300,183,43,112,158,139,184,44,115,159,140,185,45,117,160,141,186,46,118,215,214,47,187,120,161,245,247,233,219,123,142,10,181,41,156,137,111,182,42,157,138,11,180,40,155,136,178,12,38,153,134,217,205,39,154,135,179,236,241,231,229,312,310,307,315,279,196,278,277,276,283,197,282,281,280,287,198,286,285,284,291,199,290,288,289,200,295,294,293,292,297,299,201,298,296,270,271,194,269,268,274,275,195,273,272,266,267,193,264,265,255,254,190,252,253,259,258,191,256,257,263,262,192,261,260,319,320,317,318,67,18,93,49,220,222,238,243,50,1,66,17,94,48,204,210,15,95,52,4,16,64,96,53,2,51,65,14,97,3,91,59,8,55,110,92,60,6,56,108,90,58,7,54,109,62,88,13,209,212,63,89,5,57,107,61,242,237,221,227,301,316,305,302,147,22,128,165,172,148,23,129,166,173,149,24,130,167,174,150,21,131,168,175,19,151,132,169,176,170,152,20,133,177,127,145,27,216,189,213,146,206,164,218,126,144,28,163,188,143,124,26,248,234,246,228,239,232,249,230,125,25,162,171,313,314,309,311,113,32,76,77,101,114,33,79,78,102,116,34,81,80,103,119,31,82,83,104,29,121,84,85,105,86,122,30,87,106,73,202,36,72,99,74,203,37,75,100,71,235,208,70,211,9,0,207,223,244,251,224,240,225,226,250,69,35,68,98,304,306,303,308 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#2fbfbc696f8770de67b632f9354275e3bbc4952318d0e644426634c23ae4ab08, 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 22:26:51 · history