Equation 677 Database

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Magma 922f56647482…

magma 922f56647482
Size
321
Isomorphism class hash
922f56647482ab8a4cb65ad293a2b2be86b7071d53a623836f4ebd532b46979a
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 22:28:10
Display reorder
320,29,28,27,24,25,26,34,35,33,30,31,32,276,277,279,278,281,280,282,283,284,285,287,286,288,289,291,290,293,292,294,295,297,296,299,298,255,254,257,256,253,252,261,260,262,263,259,258,266,267,268,269,265,264,273,272,274,275,271,270,302,303,308,309,6,8,7,11,9,10,3,4,5,2,1,0,75,53,51,76,52,77,49,74,50,72,48,73,59,81,57,82,58,83,55,80,56,78,54,79,41,65,39,63,40,64,37,61,38,62,36,60,47,71,45,69,46,70,43,67,44,68,42,66,317,316,318,319,142,141,143,140,138,139,147,151,154,155,146,150,114,94,95,115,93,116,90,113,91,111,92,112,85,105,86,106,84,107,88,108,89,109,87,110,144,145,148,149,152,153,125,102,123,103,124,104,117,97,118,98,119,96,120,100,121,101,122,99,307,306,315,314,14,13,12,16,17,15,19,20,18,22,23,21,181,180,182,183,178,179,187,186,189,188,185,184,192,193,195,194,190,191,198,199,203,202,196,197,156,157,158,159,160,161,162,163,165,164,167,166,169,168,171,170,200,201,175,174,176,177,173,172,305,304,313,312,126,128,127,131,129,130,134,132,133,137,135,136,205,204,206,207,208,209,210,211,213,212,215,214,216,217,218,219,220,221,223,222,224,225,226,227,229,228,231,230,233,232,234,235,236,237,238,239,241,240,243,242,244,245,247,246,249,248,251,250,301,300,310,311 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#3e7f78778326128ca89bcdb69266df7c07c66aee73c2a2e36b24ead92b52079d, M = {64} 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 22:28:11 · history