Equation 677 Database

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Magma 2fb36e03b4a5…

magma 2fb36e03b4a5
Size
321
Isomorphism class hash
2fb36e03b4a50837c71b2552527219a4521137876903fdcadc9b85cce336436b
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 22:31:52
Display reorder
300,104,118,38,146,129,102,116,39,144,130,103,117,40,145,128,106,114,41,142,125,42,115,105,143,126,113,230,224,141,127,109,124,36,138,134,107,122,37,136,135,108,123,35,137,133,120,112,32,140,131,121,110,33,139,132,119,111,34,232,231,306,302,310,314,299,298,247,296,297,290,291,248,289,288,294,295,246,292,293,283,282,250,280,281,251,286,287,284,285,278,279,249,276,277,263,262,245,261,260,254,255,243,253,252,259,258,244,257,256,275,274,241,273,272,267,266,242,264,265,270,271,240,269,268,319,318,320,317,179,202,20,167,227,235,200,21,168,54,178,201,22,166,55,176,198,23,163,52,24,199,177,164,53,197,175,25,165,51,171,193,26,159,48,169,191,27,160,46,170,192,28,158,47,196,174,29,161,50,194,172,30,162,49,195,173,31,234,226,301,304,313,309,190,213,7,83,157,188,211,8,84,155,189,212,6,82,156,186,209,10,79,153,11,210,187,80,154,208,185,9,81,152,182,205,5,88,149,180,203,3,89,147,181,204,4,87,148,207,184,0,85,233,206,236,2,229,150,237,183,1,86,151,303,307,316,312,62,78,90,219,14,63,76,91,217,15,61,77,92,218,16,65,74,93,215,17,94,75,66,216,18,73,64,95,214,19,60,69,96,223,45,58,67,97,221,43,59,68,98,222,44,72,57,99,239,12,70,228,100,238,225,71,56,101,220,13,311,315,305,308 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#4ddcb3732d8cead11c348e4cf9e2318d25466469e5bf7b5d48d8ea06dbb2e5f3, 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 22:31:53 · history