Equation 677 Database

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Magma 63e33cbc19e3…

magma 63e33cbc19e3
Size
321
Isomorphism class hash
63e33cbc19e3801fa32b6a7b020a71728de506a47577a16f93cc4c1741b76786
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 22:21:07
Display reorder
300,159,68,190,121,97,160,98,66,191,122,161,96,67,189,120,100,71,158,186,124,156,101,69,187,125,99,70,157,188,123,63,165,103,181,127,64,166,104,182,128,65,167,102,180,126,164,62,106,184,130,162,60,107,185,131,163,61,105,183,129,306,304,310,303,258,173,259,257,256,261,263,171,262,260,253,255,172,254,252,271,169,268,270,269,272,275,170,274,273,267,168,264,266,265,179,281,283,282,280,177,284,287,286,285,178,277,279,278,276,293,175,295,294,292,296,176,299,298,297,289,174,291,290,288,317,318,320,319,48,47,211,209,73,49,74,45,215,214,50,72,46,207,205,76,43,51,223,222,52,77,44,227,226,75,42,53,219,218,38,54,79,235,234,36,55,80,239,238,37,56,78,231,230,57,41,82,247,246,58,39,83,251,250,59,40,81,243,242,314,313,302,301,14,34,139,193,113,12,111,35,140,194,13,112,33,138,192,109,30,17,142,196,15,110,31,143,197,108,32,16,141,195,25,20,119,137,199,26,18,117,135,200,24,19,118,136,198,23,28,115,133,202,21,29,116,134,203,22,27,114,132,201,305,311,307,312,145,90,208,8,210,146,213,91,212,6,144,206,92,204,7,221,93,148,220,11,149,224,94,225,9,217,95,147,216,10,88,151,232,233,3,89,152,236,237,4,87,150,229,228,5,154,84,245,244,2,155,85,248,249,1,153,86,241,240,0,316,309,308,315 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#07e8f68f5124a8e3a0938e8678de1c72ed7349b338061e203d5db711c48e18fa, 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 22:21:08 · history