Equation 677 Database

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Magma f98a1495031e…

magma f98a1495031e
Size
321
Isomorphism class hash
f98a1495031e800676bff69cd9693f9a25eb012fde1c967a7fec67ab3c40ef06
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 22:32:08
Display reorder
300,44,157,74,84,114,42,158,82,75,115,83,156,43,73,116,40,154,86,70,117,41,155,85,71,118,39,232,226,72,119,149,35,79,113,120,150,33,80,111,121,148,34,81,112,122,38,152,78,109,123,36,153,76,110,124,37,151,77,229,230,314,303,305,309,295,294,293,246,292,298,299,247,297,296,248,291,290,288,289,279,278,249,277,276,283,282,250,281,280,287,286,251,285,284,258,259,244,256,257,263,262,245,260,261,254,255,243,252,253,271,270,240,268,269,275,274,241,272,273,266,267,242,265,264,319,317,318,320,171,191,87,52,236,234,192,53,88,202,51,190,170,89,201,173,187,55,90,198,174,188,56,91,199,172,189,54,92,200,182,176,50,93,194,183,177,48,94,195,181,175,49,95,193,179,185,46,96,196,180,186,47,97,197,178,184,45,227,235,301,302,313,310,62,107,166,22,212,63,108,23,164,213,21,106,61,165,211,58,103,25,169,208,59,104,26,167,209,60,105,24,168,210,99,66,28,161,204,100,67,29,162,205,98,65,27,163,203,64,102,31,160,237,57,228,32,233,207,224,101,30,159,206,311,307,316,306,134,146,219,5,12,135,147,3,217,13,4,145,136,218,14,133,142,0,215,15,131,143,2,216,16,132,144,1,214,17,138,125,11,223,18,139,126,9,221,19,137,127,10,222,20,128,141,7,239,69,129,231,8,238,225,130,140,6,220,68,304,315,312,308 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#51b008b28ab03bd312921cf92cf8265fda62df0fbe14e18f3974b5c43c79b0a4, 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 22:32:08 · history