Equation 677 Database

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Magma 2aac03ad4783…

magma 2aac03ad4783
Size
321
Isomorphism class hash
2aac03ad47833560fcf6089c5e14ec7b0ed4e3ce6f830bc75e0fb2eec47b1c18
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 22:59:07
Display reorder
300,50,218,29,230,245,48,216,27,228,243,49,217,28,229,244,221,53,25,233,241,219,51,26,231,242,220,52,24,232,240,56,35,224,236,251,54,33,222,234,249,55,34,223,235,250,31,59,227,239,247,32,57,225,237,248,30,58,226,238,246,315,311,306,303,38,272,273,274,275,36,265,264,267,266,37,268,269,271,270,257,41,256,258,259,261,39,260,263,262,253,40,252,255,254,44,296,297,298,299,42,288,289,291,290,43,292,293,294,295,280,47,281,283,282,284,45,285,287,286,276,46,277,279,278,319,317,320,318,62,130,11,133,149,60,131,9,134,147,61,129,10,132,148,126,65,7,136,145,127,63,8,137,146,128,64,6,135,144,68,2,121,139,155,66,1,122,140,153,67,0,120,138,154,5,71,124,142,151,3,69,125,143,152,4,70,123,141,150,305,314,316,302,163,75,113,95,98,164,76,111,93,96,162,77,112,94,97,74,166,109,91,101,72,167,110,92,99,73,165,108,90,100,161,119,81,86,104,159,117,82,84,102,160,118,83,85,103,115,157,80,89,107,116,158,78,87,105,114,156,79,88,106,301,313,304,310,12,190,177,194,209,13,191,178,192,207,14,189,179,193,208,186,15,176,197,205,187,16,174,195,206,188,17,175,196,204,18,168,181,200,215,19,169,182,198,213,20,170,180,199,214,171,21,184,203,211,172,22,185,201,212,173,23,183,202,210,308,312,309,307 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#d958d834958932013e293186c3edbca2299f39c5df5a243bf65f8d4f2fad3f22, 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 22:59:08 · history