Equation 677 Database

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Magma 3e4d05d9e62f…

magma 3e4d05d9e62f
Size
321
Isomorphism class hash
3e4d05d9e62f1453b7ee05551caa10845da64bbc63b139d392a9e66acecc9b5c
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 22:59:52
Display reorder
300,60,237,69,115,236,61,55,113,70,51,114,232,59,68,233,2,56,111,72,54,1,57,112,73,52,0,58,110,71,53,66,6,75,106,48,67,7,76,104,49,65,8,74,105,50,62,5,78,109,47,63,3,79,107,45,64,4,77,108,46,316,315,305,308,298,299,297,240,296,291,290,241,289,288,242,294,295,293,292,283,282,243,281,280,287,286,244,284,285,279,278,245,277,276,262,263,261,246,260,255,254,253,247,252,259,258,257,248,256,274,275,272,249,273,266,267,264,250,265,271,270,268,251,269,319,318,320,317,231,15,197,122,216,229,16,123,195,214,124,17,230,196,215,18,227,125,193,219,19,228,126,194,217,20,226,127,192,218,222,13,188,120,211,220,14,186,121,212,221,12,187,119,213,225,9,191,116,210,223,10,189,117,208,224,11,190,118,209,302,303,311,309,239,238,81,28,185,204,134,29,82,183,27,234,235,80,184,136,207,31,84,181,137,205,32,85,182,135,206,30,83,180,201,133,87,26,176,202,131,88,24,174,203,132,86,25,175,200,129,90,22,179,198,130,91,23,177,199,128,89,21,178,314,307,313,306,149,158,93,36,173,147,156,37,94,171,38,157,148,92,172,161,145,35,96,169,159,146,33,97,170,160,144,34,95,168,140,153,99,42,164,138,154,100,43,162,139,155,98,44,163,143,152,102,41,167,141,150,103,39,165,142,151,101,40,166,310,304,301,312 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#e6bbf558fb3ffab686d395ed44cee4ecb6da0873fc29bc1527bdf36d2fd1603f, 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 22:59:53 · history