Equation 677 Database

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Magma 01b6771e0248…

magma 01b6771e0248
Size
321
Isomorphism class hash
01b6771e0248dad68b9c4ddd97f7f7cfece125561a7aedc32056e90b8bc31bee
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 22:21:38
Display reorder
300,144,72,161,0,68,162,145,170,69,73,163,74,146,173,67,147,160,75,175,71,148,159,76,177,227,236,239,228,178,70,142,167,77,16,66,143,168,78,17,64,141,169,79,15,65,166,139,80,1,62,164,140,81,3,63,165,235,229,221,226,316,302,311,309,278,279,22,276,277,23,282,280,281,283,21,287,286,284,285,290,18,291,288,289,294,19,295,292,293,298,20,299,296,297,271,28,270,269,268,275,29,274,273,272,267,27,266,264,265,24,255,254,253,252,25,259,258,257,256,26,263,262,261,260,320,319,318,317,34,136,89,118,238,230,222,233,154,137,88,138,33,119,155,30,92,135,120,156,31,90,133,121,157,32,91,134,122,158,38,85,128,116,152,39,86,129,117,153,37,87,130,115,151,84,35,131,113,149,82,36,132,114,150,83,223,234,232,237,306,312,305,303,5,43,97,195,194,190,6,188,184,44,96,45,4,189,183,8,93,42,186,180,9,94,40,187,181,7,95,41,185,182,11,209,48,219,218,12,215,49,207,206,10,203,50,213,212,197,14,47,251,250,247,220,224,245,244,240,13,46,201,200,313,310,308,314,107,56,2,192,193,191,108,123,171,57,98,58,109,124,172,110,99,59,125,174,111,100,60,126,176,112,101,61,127,179,105,210,54,217,214,106,216,55,205,202,104,204,53,211,208,198,102,51,249,246,248,231,225,243,241,242,103,52,199,196,307,315,304,301 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#11540e60a31227d97822464caf7bd085f23c491501101f6992da34196185b51e, 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 22:21:39 · history